Maple Flow User Manual

Copyright © Maplesoft, a division of Waterloo Maple Inc.
2024

Maple Flow User Manual
Copyright
Maplesoft, Maple, and Maple Flow are all trademarks of Waterloo Maple Inc.
© Maplesoft, a division of Waterloo Maple Inc. 2024. All rights reserved.
No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means — electronic, mechanical, photocopying, recording, or otherwise. Information in this document is subject to change without notice and does not represent a commitment on the partof the vendor. The software described in this document is furnished under a license agreement and may be used or copied only in accordance withthe agreement. It is against the law to copy the software on any medium except as specifically allowed in the agreement.
Macintosh is a registered trademark of Apple Computer, Inc.
Windows is a registered trademark of Microsoft Corporation.
Mathcad is a registered trademark of PTC Inc. or its subsidiaries in the U.S. and in other countries.
All other trademarks are the property of their respective owners.
This document was produced using Maple and DocBook.

Contents
1 Introduction ..................................................................................................................................... 1
1.1 Maple Flow ............................................................................................................................... 1
1.2 What Does This Manual Aim to Do? .............................................................................................. 1
1.3 What Is the Relationship between Maple and Maple Flow? ................................................................. 2
1.4 If You Are a Maple User .............................................................................................................. 3
1.5 Maple Flow Help System ............................................................................................................. 3
Additional Documentation ............................................................................................................ 4
1.6 Interface ................................................................................................................................... 4
Customizing the Interface ............................................................................................................. 5
Working in Maple Flow ............................................................................................................... 6
2 Canvas ............................................................................................................................................ 8
2.1 Grid ......................................................................................................................................... 8
2.2 Grid Cursor ............................................................................................................................... 8
2.3 Math and Text Containers ............................................................................................................. 8
2.4 Moving Containers ..................................................................................................................... 9Single Container ......................................................................................................................... 9Group of Containers .................................................................................................................... 9
Bringing Containers from Back to Front, and Vice Versa .................................................................. 10
2.5 Editing an Existing Container ...................................................................................................... 10
2.6 Deleting a Container .................................................................................................................. 10
2.7 Inserting or Removing White Space .............................................................................................. 10
Adding Blank Rows .................................................................................................................. 10
Deleting Blank Rows ................................................................................................................. 10
3 Entering Math ................................................................................................................................. 11
3.1 Creating a Math Container .......................................................................................................... 11
3.2 Deleting a Math Container .......................................................................................................... 11
3.3 Copying and Pasting Math .......................................................................................................... 11
3.4 Evaluating Math and Displaying Output ........................................................................................ 11
3.5 Creating Definitions and Expressing Equality ................................................................................. 11
Definitions ............................................................................................................................... 11
Expressing Equality ................................................................................................................... 12
3.6 Numeric and Symbolic Evaluation Modes ..................................................................................... 12
3.7 Numeric Formatting .................................................................................................................. 13
3.8 Basic Arithmetic ....................................................................................................................... 15
3.9 Complex Numbers .................................................................................................................... 15
3.10 Units ..................................................................................................................................... 15
Entering Units .......................................................................................................................... 15
Editing Existing Units ................................................................................................................ 16
3.11 Notes about Calculations .......................................................................................................... 17
Numerical Evaluation and Accuracy ............................................................................................. 17
Evaluation Order ....................................................................................................................... 18
Nonexecutable Math .................................................................................................................. 18
Controlling Evaluation ............................................................................................................... 18
Disabling Evaluation ................................................................................................................. 19
4 Creating a Polished Document ........................................................................................................... 21
4.1 Entering Text ........................................................................................................................... 21
Entering Math in a Text Container ................................................................................................ 21
4.2 Math and Text Styling ................................................................................................................ 21
Formatting the Content of Single Containers .................................................................................. 21
Applying Background Color to a Math or Text Container .................................................................. 21
Formatting Text ........................................................................................................................ 23iii

Contents

Applying and Changing Styles ..................................................................................................... 23
4.3 Using Sections ......................................................................................................................... 23
Controlling the Display of Sections .............................................................................................. 24
Removing a Section ................................................................................................................... 24
4.4 Controlling Display of Math ....................................................................................................... 25
Aligning Results under the Definition Operator ............................................................................... 25
Hiding Commands .................................................................................................................... 25
4.5 Controlling the Editability of a Document ...................................................................................... 26
4.6 Including Images and Drawings ................................................................................................... 26
Drawing Tools .......................................................................................................................... 26
4.7 Creating Hyperlinks .................................................................................................................. 34
Using Bookmarks ...................................................................................................................... 34
Using Shortcuts ........................................................................................................................ 36
5 Further Tools .................................................................................................................................. 38
5.1 Introduction ............................................................................................................................. 38
5.2 Functions ................................................................................................................................ 38
Maple Functions ....................................................................................................................... 38
Unsupported Maple Keywords, Commands, and Packages ................................................................ 38
5.3 More Controls for Units ............................................................................................................. 38
Setting the Default Unit System ................................................................................................... 38
Changing the Units of a Result ..................................................................................................... 39
Custom Units ........................................................................................................................... 40
5.4 Variables Manager .................................................................................................................... 41
Inserting Variables into the Worksheet Using the Variables palette ...................................................... 41
5.5 Plots ....................................................................................................................................... 41
5.6 Matrices .................................................................................................................................. 43
Entering and Using Matrices ....................................................................................................... 43
Data Import Assistant ................................................................................................................ 47
5.7 Ease of Use Features ................................................................................................................. 48
Command Completion ............................................................................................................... 48
Argument Completion ................................................................................................................ 49
5.8 Code Editor ............................................................................................................................. 50
5.9 Logging Debugging Information .................................................................................................. 50
6 Printing and Exporting to PDF ........................................................................................................... 52
6.1 Printing a Maple Flow Document ................................................................................................. 52
6.2 Print Extents ............................................................................................................................ 52
6.3 Headers/Footers ........................................................................................................................ 53
Apply a Header or Footer to All Your Documents ............................................................................ 54
Additional Options .................................................................................................................... 55
6.4 Page Setup ............................................................................................................................... 55
6.5 Print Preview ........................................................................................................................... 56
6.6 Export to PDF .......................................................................................................................... 56
6.7 Printing a Worksheet with Sections ............................................................................................... 57
7 Keyboard Shortcuts ......................................................................................................................... 58
Index .............................................................................................................................................. 62

List of Figures
Figure 1.1: Overview of in-product tutorials .............................................................................................. 2
Figure 1.2: The Maple Flow interface ...................................................................................................... 5
Figure 1.3: Options dialog ..................................................................................................................... 6
Figure 2.1: Enable/Disable Grid button on toolbar ...................................................................................... 8
Figure 2.2: Grid cursor ......................................................................................................................... 8
Figure 2.3: Flip to Front and Flip to Back buttons ..................................................................................... 10
Figure 3.1: Numeric formatting ............................................................................................................. 13
Figure 3.2: Setting default numeric formatting ......................................................................................... 14
Figure 3.3: Inserting a Unit with the Units Palette ..................................................................................... 16
Figure 3.4: Using the Unit() function to assign a unit ................................................................................ 16
Figure 3.5: Using keyboard shortcuts to insert a unit placeholder ................................................................. 16
Figure 3.6: Convert output units ............................................................................................................ 17
Figure 3.7: Numerical operations .......................................................................................................... 17
Figure 3.8: The effect of Digits on numerical accuracy .............................................................................. 17
Figure 3.9: Spatial evaluation ............................................................................................................... 18
Figure 3.10: Setting for controlling evaluation ......................................................................................... 19
Figure 3.11: Worksheet evaluation disabled ............................................................................................. 20
Figure 3.12: Visual indicator for disabled evaluation ................................................................................. 20
Figure 4.1: Entering and formatting text ................................................................................................. 21
Figure 4.2: Apply background color to a container .................................................................................... 21
Figure 4.3: Select background color ....................................................................................................... 22
Figure 4.4: A math container with background color ................................................................................. 22
Figure 4.5: The Styles drop-down list ..................................................................................................... 23
Figure 4.6: Sections in a worksheet ........................................................................................................ 24
Figure 4.7: Align Output Below := ........................................................................................................ 25
Figure 4.8: Hide commands ................................................................................................................. 25
Figure 4.9: Marker indicates hidden command ......................................................................................... 26
Figure 4.10: Drawing Toolbar ............................................................................................................... 26
Figure 4.11: Drawing on plots .............................................................................................................. 27
Figure 4.12: Help Topic Hyperlink ........................................................................................................ 34
Figure 4.13: Link To Bookmark ............................................................................................................ 35
Figure 4.14: Shortcut .......................................................................................................................... 36
Figure 4.15: Shortcut Properties ............................................................................................................ 36
Figure 4.16: Using a Shortcut to execute code ......................................................................................... 37
Figure 5.1: Setting the default unit system ............................................................................................... 39
Figure 5.2: Change units in Context Panel ............................................................................................... 40
Figure 5.3: A simple plot using a Maple plot command ............................................................................. 42
Figure 5.4: A simple 3-D plot ............................................................................................................... 42
Figure 5.5: Resizing a plot ................................................................................................................... 43
Figure 5.6: Matrix palette .................................................................................................................... 43
Figure 5.7: Matrix from palette ............................................................................................................. 44
Figure 5.8: Matrix indexing ................................................................................................................. 44
Figure 5.9: Inline Matrix Browsing ........................................................................................................ 45
Figure 5.10: Set matrix size .................................................................................................................. 47
Figure 5.11: Import data ...................................................................................................................... 48
Figure 5.12: Command completion window ............................................................................................ 48
Figure 5.13: Code Editor button on main toolbar ...................................................................................... 50
Figure 6.1: Print extents ...................................................................................................................... 52
Figure 6.2: Inserting Headers and Footers ............................................................................................... 53
Figure 6.3: Page Setup ........................................................................................................................ 56v

List of Tables
Table 1.1: How Maple Flow differs from Maple ........................................................................................ 3
Table 2.1: Container states ..................................................................................................................... 8
Table 3.1: Difference between numeric and symbolic evaluation modes ........................................................ 12
Table 3.2: Using the Command Completion feature and Expression Palette to insert a square root ..................... 15
Table 7.1: Keyboard shortcuts for canvas operations ................................................................................. 58
Table 7.2: Keyboard shortcuts for math entry ........................................................................................... 58
Table 7.3: International keyboard shortcuts for evaluation .......................................................................... 59
Table 7.4: Greek Keymap .................................................................................................................... 59
Table 7.5: Keyboard shortcuts for text entry ............................................................................................ 60
Table 7.6: Keyboard shortcuts for menu operations ................................................................................... 60
Table 7.7: Mouse bindings ................................................................................................................... 61vi

1 Introduction
1.1 Maple Flow
Maple Flow is a new calculation tool from Maplesoft. Maple Flow offers a freeform user interface combined with acomprehensive math engine. Use Maple Flow for engineering, scientific, and technical calculations and documentation.
Maple Flow gives you• A spatially aware mathematical canvas that replicates the design metaphor of a physical whiteboard• Automatic recalculation to ensure that results are always up to date
• A broad, rich mathematical language with many functions• Visually impactful, fully programmatic plots• A coding region with full access to the Maple programming language
Note for non-Windows users: The keystrokes given in this document are for Windows. If you are using a different
platform, see the keyboard shortcuts for your platform in Keyboard Shortcuts (page 58).

1.2 What Does This Manual Aim to Do?
This manual describes• The Maple Flow interface• Differences with the Maple user interface and programming language that an existing Maple user may experience.
This manual should be read in unison with the in-product tutorials and exercises; these are available from the Tutorial
link on the Maple Flow Home page. If you've closed the Home page, you can access it again from the View menu:• Select View > Home1

2 • Introduction

Figure 1.1: Overview of in-product tutorials

This manual does not describe the math functionality of the Maple Flow in detail, but makes references to specificfunctions in context of a broader discussion. The detailed documentation for the math functionality resides in the Maple
online help: http://www.maplesoft.com/support/help.

1.3 What Is the Relationship between Maple and Maple Flow?
First, some definitions:• Maple refers to the (i) Maple programming language and (ii) Maple interface.
• Maple Flow refers to the new product whose manual you are reading.
Maple Flow
• Uses the powerful Maple math engine• Borrows a few elements from the Maple interface
Maple Flow's "language" is the commands (and their syntax), data structures and programming language. These arebased on the Maple programming language; you can use any of the math functions in Maple in your Maple Flow analyses.

3 • Introduction

1.4 If You Are a Maple User
If you already use Maple, you'll appreciate the unique twist that Maple Flow offers with its spatial evaluation modeland automatic calculation updates. You will also get a head start because you'll be familiar with Maple's programming
language, functions, and features.
Maple Flow differs from the Maple interface and programming language in a number of ways. Several important differences are listed in Table 1.1.
Table 1.1: How Maple Flow differs from Maple
Maple Flow

Maple

You enter math and text at any point, simply by clicking withyour mouse, and typing.

You can enter commands at execution prompts, which arelargely aligned to the left (except when inserted into
multicolumn tables), and linearly progress down theworksheet.

This is in much the same way that you can write math at any
point on a whiteboard.
The evaluation model is forward in space. Any assignments
are only valid at any point to the right or below where they
are made.

Multiplication needs to be explicitly stated.
More numeric evaluation by default (for example 5/10
evaluates to 0.5)
Units are automatically combined. That is, N/m2 is
automatically reconciled to Pa.
What you see in the Maple Flow canvas is always up to dateand reflects the current state of all assignments. Any changes
or additions to the canvas automatically cascade down thecanvas.
Automatic recalculation means the currently visible portionof the canvas updates as you work, and as you scroll throughthe document all the calculations are updated.
Matrix, vector, and array indices are only entered with square
brackets.
Math is entered into the canvas in mathematical notation, but
programmatic content is entered in Maple notation.

The evaluation model is forward in time. You can use
assignments above or below where they are made, at any timeafter the assignment is made.
Most users progress linearly down a worksheet, but theapparently linear form of a worksheet is not always reflectedin the displayed results.
Multiplication can be implicit (i.e. entered with a space) or
explicit.
Results are kept symbolic except when requested to be numeric(for example, with the evalf command).
Units are only reconciled if explicitly requested by the user(for example, by loading a Units package).
Individual commands, groups of commands, or entire
worksheets are only updated if requested by the user. Thismeans results may not reflect the current value of definitions.

Matrix, vector, and array indices can be entered with square
brackets or typeset subscripts (in 2-D input).
Equations and programs can be entered in typeset mathematics
notation (often called "2-D math") or Maple notation ("1-Dmath").

Maple worksheets cannot be loaded into the Maple Flow, or vice versa.

1.5 Maple Flow Help System
The in-product help system, accessed through the Help menu, provides information on key commands. Each help page
gives details on the usage of a command, including the calling sequence, parameters, options, and examples.
Search: Search for a command name, keyword, or phrase.
Browse: Browse the table of contents to view a structured list of help topics.

4 • Introduction

To get help on a specific word:
1. In a worksheet, place the cursor in a word for which you want to obtain help.
2. Press F2 to access context-sensitive help.
View Help Page as Worksheet: You can open any help page as a worksheet to interact with the page and modify theexamples.
• With the help page displayed in the right pane of the help system, from the View menu, select Open Page as
Worksheet. A new worksheet window opens.
• Alternately, click Open current page as worksheet () in the help system toolbar.

Additional Documentation
Since Maple Flow uses the Maple programming language, you have the ability to use the vast math functionality thatis part of the Maple programming language. When browsing the help system, some hyperlinks take you to additional
detailed documentation for the math functionality that reside on the Maplesoft website, in the Maple online help:
http://www.maplesoft.com/support/help. Note that these pages are formatted as Maple pages, not Maple Flow pages,
so the examples will look a little different.

1.6 Interface
The different parts of the Maple Flow interface, as seen in Figure 1.2, are:
• Canvas — the workspace• Main toolbar — This toolbar is always at the top of the Maple Flow window.
• Context toolbar — This toolbar, located directly above the canvas, is relevant to the current selection.
• Palettes — In the left pane, these provide an easy way to enter a math expression, matrix, Greek letter, or units.
• Context panel — Some options relevant to the current selection appear here, such as numeric formatting and units
formatting.
• Status Bar — Displays system information

5 • Introduction

Figure 1.2: The Maple Flow interface

Customizing the Interface
Customize your Maple Flow preferences using the Options Dialog.
To open the Options Dialog:• From the toolbar, click the Options icon ().

There are six tabs.
Under the Units tab, you can specify the default unit system (SI, FPS, or IPS). For more information, see Setting theDefault Unit System (page 38).
Under the Display tab, you can customize settings related to display of output. For more information, see Numeric
Formatting (page 13) and Set Displayed Matrix Size (page 46).

6 • Introduction

Figure 1.3: Options dialog

Under the Interface tab, you can specify the following:• Open worksheets in new tab or new window.
• Open hyperlinks in new tab or new window. This refers to hyperlinks to other Maple Flow worksheets.
• Default zoom.
• Open worksheet at startup. You can select the worksheet that Maple Flow displays as the Home page. See the next
section for more information.
• Control the Automatic argument completion feature. For more information, see Argument Completion (page 49).
Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply the setting
to the current session an future sessions.
Under the Evaluation tab, you can customize settings related to evaluation. For more information, see Controlling
Evaluation (page 18).
Under the General tab, you customize settings related to saving. You can set the matrix save limit and enable savingof debugging information to a log file. For more information, see Set Matrix Save Limit (page 47) and Logging
Debugging Information (page 50).
Under the Template tab, you can customize settings related to default page layout. For more information, see Page
Setup (page 55).

Working in Maple Flow
By default, Maple Flow opens to the Home page. From this page you can access the tutorials and many sample applications. If you close this page, you can always return to the home page using View > Home.
You can customize what worksheet Maple Flow displays as the home page, or have it simply display a new, blankworksheet on start up.
• From the toolbar, click the Options icon ().

• Under the Interface tab, select the desired home page: Default home page, Specified worksheet, or New, blank.
• If you select Specified worksheet, browse to the desired document. (Tip: You may want to make your custom home
page noneditable, as described in Controlling the Editability of a Document (page 26).

7 • Introduction• Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session an future sessions.
By default Maple Flow documents open in a new tab. (That setting can be changed in the Options > Interface tab as
well.) You can always move a Maple Flow document from a tab to a new window.
To move a Maple Flow document to a new window:• Grab the document tab, and drag it onto the canvas. The document opens in a new Maple Flow window.

2 Canvas
2.1 Grid
When you drag math and text containers, the positions of containers are snapped to a grid. By default, the grid is not
displayed.
To display the grid, click the Enable/Disable Grid button on the main toolbar.

Figure 2.1: Enable/Disable Grid button on toolbar

2.2 Grid Cursor
The grid cursor is illustrated in Figure 2.2 and by default appears in the top left corner of every new canvas.

Figure 2.2: Grid cursor

The grid cursor can be moved by pointing and clicking with the mouse, or with the arrow keys.
Math and text containers are created at the location of the grid cursor.

2.3 Math and Text Containers
On the canvas, you can create math boxes or text boxes. Each box can be moved; the position of a math container determines the order in which it is evaluated (as illustrated in Figure 3.9).
A container can be in one of three states, as described in Table 2.1.
Table 2.1: Container states
Math
Stationary with no focus. A math container
in this mode is still "live", and Maple Flow
will update its result if an upstream
parameter changes.
Editing
Numeric:

Text• Only one container can be in editingmode at any one time.
• A math container has a solid dark green
border if numeric, or a dashed light green
border if symbolic (see Numeric andSymbolic:
Symbolic Evaluation Modes (page 12)).
• A text container has a blue border.
• You will see a flashing cursor, whose
position can be changed with the arrow
keys or mouse.
Move• Math and text containers that are selectedhave a light blue border. Such a container
is in move mode.

89 • Canvas

Math

Text

• One or several containers can be in movemode.
• Move the containers with the mouse.
• When instead you select using the
keyboard and Ctrl key, the container hasa royal blue border.
• Move the container with Ctrl + arrowkeys.

2.4 Moving Containers
Single Container
With the mouse
To move a container with the mouse:
1. Move the mouse pointer over a container.
2. Move the container to another position by click and dragging.
3. Release the mouse button when the container is in the desired position.
With the keyboard arrows
To move a container with the keyboard:
1. Move the grid cursor into a container so that the container is in editing mode.
2. Do one of the following:• Press Ctrl and use the arrow keys to move the container one grid space at a time.
• Press Ctrl + Shift and use the arrow keys to move the container a single pixel at a time.
Note that when you press Ctrl, the container border changes to royal blue to indicate Ctrl has been pressed.

Group of Containers
To move multiple containers:
1. Click in a blank part of the canvas.
2. Drag a selection box around a group of containers.
3. Release the mouse button.
Alternatively, you can press and hold Ctrl while you select the containers.
4. Move the mouse pointer over one of the selected containers.
5. Drag the containers to another location.
To align containers:
1. Click in a blank part of the canvas.
2. Drag a selection box around a group of containers.
3. Release the mouse button.
4. Right-click and from the context-sensitive menu, select Align Left.

10 • Canvas

Bringing Containers from Back to Front, and Vice Versa
You can potentially have two containers at the same grid position.You can bring the lower container forward, or send
the top container back, by using Flip to Front and Flip to Back buttons.

Figure 2.3: Flip to Front and Flip to Back buttons

2.5 Editing an Existing Container
To enter editing mode on an existing container, do one of the following:• With the mouse, click the container.
• With the arrow keys, move the grid cursor onto the container.

2.6 Deleting a Container
To remove a container, do one of the following:• With the mouse, select the container (or containers) and from the toolbar, select Cut ()• Move the grid cursor into a container so that the container is in editing mode. Then press Ctrl + Delete to delete thein-focus container.
• Triple-click the container to select the entire container, then press Delete.

2.7 Inserting or Removing White SpaceYou can insert or remove space in the canvas (i.e. grid rows) by using the Enter, Backspace, and Delete keys.

Adding Blank Rows
To add blank rows, place the grid cursor on a blank part of the canvas and press Enter. This shifts all content on andbelow the same row as the grid cursor down.

Deleting Blank Rows
To delete blank rows, click on a blank row of the canvas and press one of the following:• Backspace to remove that blank row and shift the grid cursor and all content below the grid cursor up.
• Delete to remove that blank row, and shift all content below that row up.

3 Entering Math
3.1 Creating a Math Container
A math container is a box in which you enter math that is to be evaluated.
To create a math container:
1. Click on a blank part of the canvas.
2. Begin typing your math. As soon as you enter the first character, a math container is created automatically.

3.2 Deleting a Math Container
To delete a math container, do one of the following:• Drag-select the math container and press Delete.
• In editing mode, press Ctrl + Delete to delete the in-focus container.
• Triple-click the container to select the entire container, and then press Delete.

3.3 Copying and Pasting Math
When you are copying from outside of Maple Flow, for example from a text document, by default the content is pasted
into your Maple Flow worksheet as text. If you are copying a math expression, there is an easy way to ensure it pastes
as math.
To copy and paste as math:• Select and copy the math.
• To paste as math, right-click on a location in the worksheet, and select Paste as Math.
A new math container is created, and the selected math is copied into it.

3.4 Evaluating Math and Displaying Output
Anytime you leave a container by pressing Enter, or navigating away using Tab or the arrow keys, evaluation occurs.
All math is evaluated in the canvas, using a left-to-right, top-to-bottom order (see Evaluation Order (page 18)). When
you need to display results, evaluate and display output.
To evaluate math and display results:• Enter the expression, then press =. The evaluation occurs and the result displays. The focus remains in the mathcontainer.
If desired, press Enter or the arrow keys to leave the math container.
Typically all visible calculations that are dependent on a math container are updated when the focus leaves a mathcontainer.
You can change the behavior of = in a math container, if desired. See Controlling Evaluation (page 18).

3.5 Creating Definitions and Expressing Equality
Definitions
You can assign a numerical value or an expression to a name by using := (a colon, followed by an equal sign).

1112 • Entering MathFor example, enteringin a math container assigns the value 4 to the name a.

You can then use this definition later.

Expressing Equality
As discussed in Evaluating Math and Displaying Output (page 11), by default the equal sign is used to evaluate anddisplay results. When you are entering an expression into a math container that involves an equation, use Ctrl + = toenter the equal sign. This allows entry of the = symbol without immediate evaluation of the math container.
Example 1.
Solve this equation for x:
A one-line solution is:

Notice there are two equal signs in this math container. The first one is part of the equation. The second one means
evaluate and display results, and at the end you see the two solutions: 3.828 and -1.828.
An alternative approach is to first define the equation, then solve for the result.

In both cases, use the following steps:• To enter the equal sign between the left-hand side and right-hand side of the equation, use Ctrl + =.
• To enter the equal sign that means evaluate and show results, use =.
Example 2.
When the calling sequence for a command includes an option of the form name=value.
For example, on the CurveFitting:-LeastSquares help page, there is an example using the option weight:

In this example, use Ctrl + = to put the equal sign in weight=[1, 1, 1, 10].
When View > Visual Indicators is selected, the = for equality is displayed in bold. For more uses of the visual indicators setting, see Hiding Commands (page 25).
You can change the behavior of = in a math container, if desired. See Controlling Evaluation (page 18).

3.6 Numeric and Symbolic Evaluation Modes
Maple Flow offers two math evaluation modes—numeric and symbolic.
Table 3.1: Difference between numeric and symbolic evaluation modes
Numeric evaluation mode

Symbolic evaluation mode

13 • Entering Math

The numeric evaluation mode performs as much numeric evaluation as possible. For example:• Rational fractions (such as ½) are converted to floating-point numbers• Pi and exp(1) evaluate to floating-point numbers
Symbolic evaluation mode prevents numeric evaluation (except when requested by the user). For example:• Rational fractions are only converted to floating-point numbers if request by the user (e.g. with the evalf command)• Pi evaluates to a symbolic name
In both modes, unassigned names are evaluated symbolically (i.e. in numeric mode, unassigned names do not give anerror when evaluated).
The current mode of an existing math container is given by clicking inside it, and observing the state of the border or
Numeric/Symbolic buttons in the Context toolbar, as illustrated in Table 3.1.
By default, new math containers are numeric. Clicking the Symbolic button in the Context toolbar switches the in-focus
math container to symbolic mode. Alternatively, use the shortcut key Alt + S.
Holding down the Symbolic button for a second makes symbolic evaluation mode "sticky". This is indicated with apadlock by the Symbolic button (). This means that all future math containers will be symbolic (until symbolicmode is toggled off, by toggling to Numeric, or with another long click on the Symbolic button).

3.7 Numeric Formatting
By default, Maple Flow displays numeric results with three decimal places. To customize the numeric formatting:
1. Place the editing cursor on a numeric result.
2. Use the Number Format options in the Context Panel.

Figure 3.1: Numeric formatting

Note that the number format options in the Context Panel only apply to a single math container.
To select a number format and apply it broadly, you can use the Options Dialog to set your desired number format andapply it either to the current session or globally.
1. From the toolbar, click the Options icon ().

2. Under the Display tab, select the desired number format.

14 • Entering Math

3. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.

Figure 3.2: Setting default numeric formatting

Maple Flow supports the following standard number formats:• Fixed• Currency• Scientific• Engineering• Percent
You can also create a Custom format.
To apply a custom format to a single math container:
1. Place the cursor in the numeric result to be formatted.
2. In the Context Panel, under Number Format, select Custom. In the custom string field you can enter a string thatis specific to your formatting needs.
Examples include the following:• #.### formats to 3.12
• 00.000 formats to 03.120• #,#.# formats to 2,100,320.5• $0.00 formats to $123.50• ??0.00;[Red](??0.00) formats to blue for a positive number, and red for a negative number• [<10]Low;[>=100]High;Medium formats to "Low" for numbers less than 10,"High" for numbers less than orequal to 100, and "Medium" otherwise
To apply a custom format to all numeric results in the current session or globally:
1. From the toolbar, click the Options icon ().

2. Under the Display tab, for Number Format select Custom and enter your specification in the custom string field.
3. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.
To remove a number format, return to the Number Format dialog and select None.

15 • Entering Math

3.8 Basic Arithmetic
Equations are entered in typeset math notation, using standard keys such as /, *, + and -.
Note that multiplication must always be explicitly stated. For example, you must enter 3*x, not 3x.
You can also use the Expression palette or Command Completion feature to enter typeset math, as illustrated in Table
3.2.
Table 3.2: Using the Command Completion feature and Expression Palette to insert a square root(a) Command completion(b) Expression palette

For more information on command completion, see Command Completion (page 48).
When you select a template, you can then replace the placeholders in the template, using Tab to move between placeholders.
Tips on piecewise functions: You can enter a piecewise function using the Expression palette or command completion.
To add an additional line to the piecewise function, place your cursor in the piecewise function and right-click. Fromthe context menu, select either Insert Row Above or Insert Row Below. Similarly, you can remove a row using Delete
Row in the same context menu. Triple-click to select the entire piecewise function.

3.9 Complex Numbers
Imaginary numbers are entered with a number followed by the suffix i, with no multiplication between the two. For
example, 2+2i.
The unit complex number is created with 1i. You cannot just enter i for the unit complex number.
To create a symbolic multiplier on an imaginary number, you need to enter x*1i.

3.10 UnitsEntering Units
You can enter units in several different ways.

16 • Entering Math

Units Palette
You can enter units using the Units palette located in the Palettes pane on the left side of the Canvas. Click the desired
unit (using the Dimensionality drop-down list to switch to different groups of units), or insert the unit placeholder (asillustrated in Figure 3.3) and overwrite the placeholder.
You may want to place a space between the number and the unit.

Figure 3.3: Inserting a Unit with the Units PaletteUnit function
You can use the Unit() function to assign a unit.

Figure 3.4: Using the Unit() function to assign a unit

Keyboard shortcut
Press Ctrl + Shift + U to enter a unit placeholder. Then, replace the placeholder with the desired units.

Figure 3.5: Using keyboard shortcuts to insert a unit placeholder

Editing Existing Units
Move the cursor onto the unit. When the unit has focus, it is highlighted by a light blue box. You can now change theunit.
Deleting all the characters in a unit placeholder will leave an empty placeholder one character in size. Deleting thisempty placeholder will remove the unit placeholder entirely.
When the results of your calculations contains units, you can use the units formatting options in the Context Panel torescale the units to units you'd prefer to see.

17 • Entering MathFigure 3.6: Convert output units

Further tools for working with units are described in More Controls for Units (page 38).

3.11 Notes about Calculations
Numerical Evaluation and Accuracy
Any purely numerical operations are evaluated to a floating-point approximation.

Figure 3.7: Numerical operations

The Digits environment variable controls the number of digits that Maple uses when making calculations with software
floating-point numbers.
The default value of Digits is 10. The value of Digits is changed with the assignment operator (e.g. Digits:=15).
Figure 3.8 illustrates the effect of changing digits from its default value of 10 to 15 on the evaluation ofthat numeric formatting on the result ofhas been set to Fixed with 20 decimal places.)

Figure 3.8: The effect of Digits on numerical accuracy. (Note18 • Entering Math

Evaluation Order
Maple Flow evaluates calculations from left-to-right, top-to-bottom (much like reading a page from a book). Thismeans that downstream calculations only "see" assignments on the left or above. This is illustrated in Figure 3.9.

Figure 3.9: Spatial evaluation

You can change the evaluation order by moving math containers around.

Nonexecutable Math
You may want to enter nonexecuting math for documentation purposes. You can do this by entering math into a text
container. For details, see Entering Math in a Text Container (page 21).

Controlling Evaluation
By default, Maple Flow recalculates all visible dependent containers when a math container is created, edited, or moved.
You can also force evaluation when your cursor is in a math container by using Ctrl + Enter.
When the calculations are in progress, the status bar at the bottom of the Maple Flow window displays a status message:
Evaluating... m/n where n is the total number of math containers being evaluated.
To stop the current calculation:• From the toolbar, click the Interrupt icon,.

The Options dialog contains settings you can control related to evaluation.
If you want the entire worksheet to be updated when you make an edit, you can change the settings to recalculate alldependent containers in the entire document, rather than just visible containers.
1. From the toolbar, click the Options icon ().

2. Click on the Evaluation tab.
3. Under Content to evaluate, select one of the following:• Evaluate only visible containers (the default)• Evaluate all dependent containers
4. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.

19 • Entering MathFigure 3.10: Setting for controlling evaluation

Under the Options > Evaluation dialog, you can also change the meaning of = in a math container. Under Evaluation
keys, select one of the following:• = to evaluate math and display results, and Ctrl + = for equality (the default). When typing in a math container
in this mode, at any location you can use the = key to have the math container evaluate and show results. Ctrl + =is used to type an equal sign without causing immediate evaluation.
• = + Enter at the end of math to evaluate and display results, and = for equality . The equal sign can by typed
without causing an evaluation. To get a math container to display results, enter the expression, then with the cursor
at the right end of the expression, press =, followed by Enter (or move the focus outside of the container).
After you make your selection, click Apply to Session or Apply Globally.
Under Options > Evaluation, you can control whether a worksheet is executed when it is opened. Under When loadinga worksheet, select one of the following:• Don't execute the worksheet (the default)• Execute the worksheet
If Execute the worksheet is selected, when a file is opened, for consistency between saved results and worksheet
display settings, auto-evaluation on load happens if needed. For instance, this would ensure output units and matrices
are displayed according to the current settings.
If Don't execute the worksheet is selected, no auto-evaluation happens on load.
After you make your selection, click Apply to Session or Apply Globally.

Disabling Evaluation
If you want to author content without any math evaluating in the Maple Flow worksheet, but eventually the math will
be executed, you can temporarily disable evaluation.
To disable evaluation:• Click Turn evaluation off (Disabled.

) on the toolbar. An indicator appears at the top of the canvas indicating Evaluation

20 • Entering MathFigure 3.11: Worksheet evaluation disabled

To enable evaluation:• Click the icon again.
To disable evaluation of a single math container:• Right-click on the container and from the context menu, select Disable Evaluation.
There is an option to display a visual indicator for math containers that have evaluation disabled. To enable this setting,select View > Visual Indicators. When Visual Indicators is selected, a math container with evaluation disabled isdrawn with a red circle at the top left corner.

Figure 3.12: Visual indicator for disabled evaluation

To show the command again, right-click and clear the Disable Evaluation check box from the context menu.

4 Creating a Polished Document
4.1 Entering Text
To enter text:
1. Click in a blank part of the canvas.
2. Press Space to create an empty text container. This will have a blue border.
3. Type your text.
4. Use the context toolbar to format your text.

Figure 4.1: Entering and formatting text

Spellcheck is available through the Tools menu.

Entering Math in a Text Container
You may want to enter nonexecuting math for documentation. You can do this by entering math into a text container.
To enter math in a text container:
1. Anywhere inside a text container, press Ctrl + R to switch into math mode.
2. Enter your math.
3. If required, press Ctrl + T to return to text mode.

4.2 Math and Text Styling
Formatting the Content of Single Containers
To change font, size, and font color, drag-select the content and use the context bar.

Applying Background Color to a Math or Text Container
Math and text containers can also have a background color. This can be useful, for instance, to highlight a math container that contains the assignments for the variables that are used in the later calculations.
To apply a background color, right click on a container.

Figure 4.2: Apply background color to a container

2122 • Creating a Polished Document

The color selector dialog appears. Select a color.

Figure 4.3: Select background color

To apply a background color to multiple math containers, select the math containers, then right-click and from thecontext-sensitive menu, select Background Color.
Figure 4.4 shows the result of using a background color on the math containers that define two assignments, and another color on the plot.

Figure 4.4: A math container with background color

For information on creating plots, see Plots (page 41).

23 • Creating a Polished Document

Formatting Text
In text containers, you can control the formatting of text.
In the Format menu, the Character submenu can be used to apply bold, italic, underline, or strikethrough to text, tomake a subscript or superscript in the text, or to change the text color or highlight text.

Applying and Changing Styles
The style drop-down list contains several formatting styles for text and math.

Figure 4.5: The Styles drop-down list

By default:• Text is given the Text style.
• Math input is given the 2D Math style.
• Math output is given the 2D Output style.
You can apply other styles with the other entries (such as the Title style for text). You will need to select the content
and then pick the appropriate style. You can select text by clicking in the container and then using Edit > Select Allor drag-select.
Use the Format > Styles menu to change the typeface of the pre-defined styles.
Use the Format > Manage Style Sets menu to:• Export and save the active style set.
• Load and apply an existing style set.

4.3 Using Sections
You can use sections to organize your document.
To create a section:
1. Select Insert > Section.
If you select some content and then use Insert > Section, the selection will be enclosed in the section.
2. Enter a title for the section. You can modify the font/style for the title.
To change the size of the section, you can drag the bottom boundary line. If you drag the section boundary past additional content, the section now encloses that content.
To collapse a section:• Click the collapse button ().

To expand a section:• Click the expand button ().

24 • Creating a Polished Document

Figure 4.6 shows an example of a Maple Flow worksheet with sections. The first section is collapsed and the second
section is expanded.

Figure 4.6: Sections in a worksheet

Evaluation order still applies as it normally does, and content in a section is evaluated even if a section is collapsed.

Controlling the Display of Sections
You can edit a section title by clicking in the text box for the title, or by clicking on the top boundary line.
Tip: If a section does not have a title, click on the top boundary line. This opens the title text box for editing.
You can control the display of sections using Format > Section Style. From this dialog, you can• Control whether to display the top and bottom boundary lines.
• Control whether boundaries are displayed on only the left-most page.
• Specify margins.
• Specify boundary line thickness.
• Specify boundary line color.
• Specify boundary opacity.
• Control whether to display the expand button.
Note that if the section style is set up so the expand/collapse button is not displayed, you can expand or collapse a
section by doing one of the following:• Click the left most part of the top section boundary line
• Double-click anywhere along the top section boundary line.
For information on controlling the display of sections when printing or exporting to PDF, see Printing a Worksheetwith Sections (page 57).

Removing a Section
To remove a section:• Use Edit > Remove Section. The content remains in the canvas, and the section boundaries are removed.

25 • Creating a Polished Document

4.4 Controlling Display of Math
When creating a document, you can control some aspects of the display of the content of math containers. For instance,
you can control numeric formatting, as described in Numeric Formatting (page 13). This section describes some further
customizations.

Aligning Results under the Definition Operator
Typically, math output appears inline with the input. In the case that you are making a definition and displaying theoutput, you can choose instead to align the result on a new line, under the definition operator. This can help withreadability. Figure 4.7 shows an example in which the output of the stress definition is displayed below.

Figure 4.7: Align Output Below :=To align the result on the next line, below the := operator:
1. Enter the definition and press = to evaluate and display results.
2. With focus in the math container, click Align math output on newline (now on a newline, aligned with the definition operator.

) in the context toolbar. The result is

Hiding Commands
When creating a document, you can hide the input expression and just show the resulting output.
To hide the input expression:• Right-click on the math container and select Hide commands from the context menu.
In the case of an assignment, you can select either Hide commands or Hide commands and name.

Figure 4.8: Hide commands

There is an option to display a visual indicator for math containers that have hidden commands. To enable this setting,select View > Visual Indicators. When Visual Indicators is selected, a math container with hidden commands is drawn
with a gray circle at the top left corner.

26 • Creating a Polished Document

Figure 4.9: Marker indicates hidden command

To show the command again:• Right-click and select Show commands from the context menu.
Similarly, you can select Show name if the name has been hidden.
You can also perform the hide commands action on multiple math containers.
1. Drag a selection box around a group of math containers.
2. Release the mouse button.
3. Right-click and from the context menu select Hide commands or Hide commands and name.

4.5 Controlling the Editability of a Document
You can protect the content in a document from changes by marking either the entire document as noneditable.
When a document is marked as noneditable, existing content in the document cannot be modified. For example, theHome page that appears when you first open Maple Flow is a noneditable document.
To prevent changes to a document, ensure the document is noneditable:• In the status bar at the bottom of the Maple Flow window, clear the Editable check box.
When a document is noneditable, users can view the document, open and close sections, and click links, but cannotchange content.
To change any part of a document, ensure the document is editable:• In the status bar at the bottom of the Maple Flow window, select the Editable check box().

4.6 Including Images and Drawings
You can insert images and drawings into your worksheet using Insert > Image and Insert > Drawing.
When you insert a drawing, an empty grid appears. You can then use the drawing tools. You can also use the drawing
tools on an image or a plot.
You can resize an image or drawing using the grab box around the image. Tip: To maintain the aspect ratio on an image,use the corner resizing handles. To maintain the aspect ratio on a drawing, hold the Shift key while resizing.

Drawing Tools
To view the drawing tools, select a drawing or an image in your Maple Flow worksheet. The Context toolbar displays
the Drawing toolbar.

Figure 4.10: Drawing Toolbar

27 • Creating a Polished Document

Drawing on Plots
To view the drawing tools on a plot, select the plot in your Maple Flow worksheet. The Context toolbar displays the
Plot toolbar by default. Use the drop-down list to switch to the Drawing toolbar, as shown in Figure 4.11.

Figure 4.11: Drawing on plots

Available Tools
The tools include the following: selection tool, pencil (free style drawing), eraser, text insert, straight line, rectangle,
rounded rectangle, oval, diamond, arc, alignment tool, drawing outline tool, drawing fill tool, and line style tool.
Tip: For the text, line, rectangle, round rectangle, oval, diamond, and arc tools,- Click once on the toolbar icon to insert that type of object into the drawing. The tool is activated. For example,.
- Click twice on the toolbar icon to insert multiple objects of the same type without having to reselect the tool.
The icon is highlighted yellow. For example,
icon.

. The tool remains activated until you select another toolbar

Text

To insert text in the drawing canvas:
1. Click the text icon ().

2. Click in the drawing canvas (on the image). A text box appears.
3. Enter text and modify font as necessary using the toolbar font and font size drop-down lists. Include math in the
text box in the same way you include math in a text container. See Entering Math in a Text Container (page 21).
4. Optional. Select a fill color for a text box or select the line color for the border in the same way it is done for objects.

28 • Creating a Polished Document

Lines - Straight, Resizing, Adding Arrows
Drawing Straight Lines
To draw a straight line:
1. Click the straight line icon ().

2. (Optional) From themenu, select the line style, thickness, and arrow points:

3. In the canvas, click and drag the mouse. A straight line is drawn.
4. To complete the line, click the mouse twice or press Enter. The drawing feature switches to the Selection tool.
5. You can draw more than one connected line; to complete your drawing, click the mouse twice, press Enter, or bringthe end of the last line back to the start of the first line.
6. To remove the last point drawn, press Esc.
Drawing a Line that Snaps to Vertical, Horizontal, or a 45 Degree Angle
To draw a line that snaps to an orientation that is a multiple of 45 degrees:
1. Click the straight line icon.
2. In the canvas, click and drag the mouse.
3. Press and hold the Shift key to snap to a 45 degree increment.
4. To complete the line, click the mouse twice or press Enter.
Drawing a Line that is Attached to a Shape
To draw a line that is attached to a shape in the drawing canvas:
If you have inserted a shape in the canvas, you can draw a line that is automatically attached to that shape.
1. Click the straight line icon.
2. Press and hold the Ctrl key, and, in the canvas, hover your mouse cursor over the existing shape to which you want
to attach the line. The shape is highlighted in green.
3. To draw the line, click and drag the mouse.
4. To complete the line, click the mouse twice or press Enter. The drawing feature switches to the Selection tool.

29 • Creating a Polished Document

Resizing Lines
To resize objects drawn with straight lines:
1. Select the line to be resized using the selection tool.
2. With the mouse pointer over a grab box, click and drag the line to increase or decrease its size.
3. Release the mouse button.

To resize a shape and maintain the aspect ratio, hold the Shift key while resizing.
Changing Vertices of Lines
To change vertices of drawn lines in the canvas:
When an object is selected, grab boxes and nodes at the vertices are displayed.

1. Click a node and drag the mouse to the desired point, thereby changing the vertex position.
2. Release the mouse.
Changing the Line Style
To change the style of drawn lines:
You can change the line style, thickness, and arrow points of a line either when it is drawn or afterwards.
1. Select a line using the selection tool.
2. From themenu, select a line style, thickness, or arrow direction and shape.

30 • Creating a Polished Document

The selected change is automatically applied to the straight line.
For example, a straight, thick line will have a solid arrow on the right end after clicking on the menu item displayed
above.

Rotating Images or Rotating Objects in a Drawing
You can rotate an image, or an object in a drawing. The process is the same.

To rotate an object:
1. Select the object. The vertices of the object are designated by grab boxes.
2. Place the cursor at one of the vertices.
3. Press Ctrl. The rotate icon is displayed.
4. While pressing Ctrl, click the mouse and drag. The object rotates. Release the mouse once the object is positioned
as you want.

31 • Creating a Polished Document

Color Selection Dialog
The drawing outline tool, drawing fill tool, and canvas properties tool allow you to select colors for shapes, lines, andthe canvas grid lines. Choose a color by using one of the following tools in the color selection dialog:
Color Palette

To select a color, click a color from a palette of pre-defined colors.
The last five colors that you select are displayed in the box below the color swatches. If you want to view the RGB
values of a particular color, hover your mouse cursor over a color swatch.
Color Wheel

To select a color:
1. Move the slider beside the color wheel to display a range of colors.
2. To select a color, click a point in the color wheel.

32 • Creating a Polished Document

Color Value Sliders

To select a color, specify the RGB values of the color by moving the sliders. Alternatively, you can use the spinners
to scroll to certain values or type the values directly in the fields. For each RGB value, you can specify a number from0 to 225.
Color Magnifying Glass

To select a color:
1. Select the eye dropper icon ().

2. Hover the color magnifying glass over an area on your screen that displays the color you want to select.
3. Using your mouse cursor, in the circle, click a point that displays the color.
To cancel your selection, right-click the circle.
Pencil Tool - Free Form drawing
To draw with the pencil tool in the canvas:
1. From the drawing icons, select the pencil tool icon ().

2. Click and drag your mouse in the canvas to draw lines. Release the mouse to complete the drawing.
Selection Tool - How and When to Use
To select items in the canvas use the selection tool ().

You can use the selection tool to select a single object or a group of objects. To select a group of objects:
Using the selection tool, click and drag the mouse around the items to be grouped. Release the mouse button. The items
are temporarily grouped.
Apply formatting as desired, for example by using the alignment tools in the Drawing toolbar.

33 • Creating a Polished Document

To temporarily switch to the selection tool (when using another tool), press and hold the Tab key (Command, Mac).
You can move and resize objects. When you release the Tab key, the tool will revert to its previous setting. This allows
you to tweak something you just drew.
Filling Objects - Solid or Gradient Fill Colors
Filling an Object with a Solid Color
To fill an object with a solid color:
1. Select the object in the canvas.
2. From themenu, select the solid fill style at the top (next to None).

3. From the same menu, click the left color bar at the bottom, and select a color from the color palette.

4. To change the line color, select a color from themenu.

Filling an Object with a Gradient Color
To fill an object with a gradient color:
1. Select the object in the canvas.
2. From themenu, select one of the gradient fill styles, the square icons.

3. From the same menu, click the left and right color bars at the bottom to select a color from the color palette for eachpart of the gradient.

34 • Creating a Polished Document

See below for instructions on filling an object with an image.

4.7 Creating Hyperlinks
You can add a hyperlink to a worksheet that links to another Maple Flow worksheet, a webpage, and more.
To insert a hyperlink:
1. In a text container, select Insert>Hyperlink. The Hyperlink Properties dialog opens.
2. For the Link Text field, enter the text to be shown.
3. Select the link type.
4. For the Target field, enter the destination. Note that you have to save your document if you want to use a relativepath.
5. Optionally, you can add a hyperlink tooltip.
You can also create a hyperlink by selecting some text and using the Format > Convert > Hyperlink menu item.
To edit the hyperlink properties, right-click on the hyperlink and select Hyperlink Properties.
You can create a hyperlink to a Maple Flow help page. For example, setting Type to Help Topic and Target to solve
creates a link to the solve help page.

Figure 4.12: Help Topic Hyperlink

Using Bookmarks
Bookmarks allow you to mark a specific position in a worksheet. After you have created a bookmark, you can createa hyperlink to that bookmark.
You can create a bookmark for a section title, text container, math container, or image.

35 • Creating a Polished Document

To create a bookmark:1. Place the cursor at the location where you want the bookmark.
2. From the Format menu, select Bookmarks. The Bookmarks dialog opens.
3. Click New. The Create Bookmark dialog opens.
4. Enter a bookmark name and click Create. The new bookmark appears in the Bookmark dialog list. Click OK toaccept this bookmark.
You can link to a bookmark using a hyperlink. You can link to a bookmark in the same worksheet or in anotherworksheet.
To create a link to a bookmark in the same worksheet:
1. In a text container, select Insert>Hyperlink. The Hyperlink Properties dialog opens.
2. For the Link Text field, enter the text to be shown.
3. Select Worksheet from the Type drop-down menu.
4. Leave the Target field blank to link to a bookmark in the current document.
5. From the Bookmark drop-down menu, select the desired bookmark. All bookmarks in the current worksheet areavailable.

Figure 4.13: Link To Bookmark

6. Optionally, you can add a hyperlink tooltip.
7. Click OK. The hyperlink is created.
You can also create a hyperlink to a bookmark by selecting some text and using the Format > Convert To > Hyperlink
menu item.
To create a link to a bookmark in another worksheet, the steps are analogous, but for the Target field, enter or browse
to the desired Maple Flow worksheet.

36 • Creating a Polished Document

Additional Notes:• The Edit > Go To menu item can be used to go to a bookmark in the current worksheet.
• You can rename or delete an existing bookmark from the Format > Bookmarks menu.
• There is an option to display a visual indicator for bookmarks. To enable this setting, select View > Visual Indicators.
When Visual Indicators is selected, a container or other location in the document that has a bookmark is drawn witha dark gray square at the top left corner.

Using Shortcuts
In addition to hyperlinks, your worksheet can contain shortcut components, which are clickable image links. The default
look of a shortcut is shown in Figure 4.14, but you can change the image used. The Application Gallery in Maple Flowuses shortcuts.

Figure 4.14: Shortcut

To insert a shortcut:
1. Click on the canvas.
2. Select Insert > Shortcut. A shortcut component is inserted at the cursor.
3. To edit the shortcut properties, select the shortcut component, and in the Context Panel the shortcut properties areavailable.

Figure 4.15: Shortcut Properties

4. Specify a caption, which appears below the image. Optionally, add a tooltip.
Note: The Name field is used by Maple Flow to identify the component. The caption is what is visible.

37 • Creating a Polished Document

5. Specify a link target. You can link to a Maple Flow worksheet or URL. You can also use the Shortcut to open ablank Maple Flow worksheet, execute one line of Maple code, or open a help topic.

Figure 4.16: Using a Shortcut to execute code

6. If desired, change the image.

5 Further Tools
5.1 Introduction
This chapter provides further details on a range of tools available in Maple Flow, including mathematical functions,plots, using units in Maple flow, working with matrices, features that make authoring documents easier, and programming
via the code editor.

5.2 Functions
Maple Functions
Maple Flow is built on top of the Maple programming language. You can use most Maple functions in Maple Flow.
Maple package functions are used in the long form. For example, SignalProcessing:-FFT(). Note: Use of the with()command to load packages is not supported.
The Maple programming language is described in the Maple online help: http://www.maplesoft.com/support/help.

Unsupported Maple Keywords, Commands, and Packages
As noted above, the with() command is not supported, and instead package commands should be called using the longform of their name. In addition, some Maple keywords, commands, and packages are not supported. The following
are some examples, but not a complete list.
The assume command is not supported (use assuming instead). Some keywords, such as read and save, are not supported.
These Maple packages are not supported:• Physics• Tolerances• DocumentTools• Typesetting
Procedures can only be defined in the Code Editor. See Code Editor (page 50).

5.3 More Controls for UnitsIn Units (page 15), we describe how to add units to your computations. In this section we describe further tools forcontrolling units in your computations.

Setting the Default Unit System
By default, units in output are displayed using the SI system of units. You can change the default system of units.
To set the default system of units:
1. From the toolbar, click the Options icon ().

2. Under the Units tab, select the desired output unit system, SI, FPS, or IPS.
3. Select Apply even if no operations are performed to force recalculation of the worksheet.
4. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.

38

39 • Further Tools

Figure 5.1: Setting the default unit system

This will not modify any units that have had units formatting applied directly as described Editing Existing
Units (page 16).

Changing the Units of a Result
Sometimes you want to control the units displayed in a result beyond setting the default system of units. There are two
ways of changing the units of a result: inline or through the Context Panel.
To change the units of a result inline:
1. Move the cursor into the output of the math container.
2. Delete the existing unit, and type the desired unit.
3. Press Enter or use the arrow keys to leave the math container. The result is updated.
For example, in this example, suppose we want the elapsedtime shown in minutes, not seconds.

Edit the right-hand side by deleting the unit s and typing min. When you press enter the result is calculated in the desired
units.

To change the units using the Context Panel:
1. Move the cursor into the output of the math container.
2. In the Context Panel for the result, select the desired unit from the Choose Unit list, and press Enter. You can also
type the desired unit in the Enter Unit field, for instance, if the Choose Unit list doesn't show the desired unit, as
the list is not exhaustive.

40 • Further Tools

Figure 5.2: Change units in Context Panel

Dimensional Balancing
If you change a unit of a result inline or via the Context Panel, and the unit is dimensionally inconsistent with the currently
displayed unit, Maple Flow automatically performs dimensional balancing by inserting additional units to make theresult dimensionally consistent.

Custom Units
You can define a custom unit, which will then be available for rescaling any result with units of equivalent dimension.
To define a unit:
1. Click a blank part of thecanvas to create a mathcontainer, and then from theUnits palette insert the units
placeholder.

2. In the units placeholder, typethe name of your custom unit.
3. Use the right arrow key toleave the units placeholder.
4. Type := (colon equals) tocreate a definition.
5. Insert another units
placeholder from the Units
palette.
6. Enter the unit definition.

fpd can now be used to rescale any result with a dimension equivalent to length/time.

41 • Further Tools

5.4 Variables Manager
The Variables Manager in the palettes pane helps you keep track of the variables currently defined in your worksheet,including any defined custom units.
As you move your cursor through the worksheet, the Variables manager dynamically updates to show what variables
are defined up to that point.
ButtonFunction
View - Inspect the value assigned to avariable.
Hide - Hide a variable in the Variable
Manager
Filter - Filter the variables list so theselected variables are shown.
This can be used to unhide a variable
you previously hid.

Inserting Variables into the Worksheet Using the Variables palette
Any variables that appear in the Variables palette can be inserted into the worksheet from the palette.
To insert a variable from the Variables palette into your worksheet, either:• Right-click on a variable, then from the context menu, select Insert Into Worksheet.
or• Double-click on the variable name in the Variables palette.
Notes:
Insert Into Worksheet is enabled only when:• The grid cursor is on the canvas. In this case, a new math container is created into which the variable being inserted
is added.
• The cursor is currently in an active math container. In this case, the variable is inserted at the cursor location.

5.5 Plots
You can create a plot with the Maple language plot command. A simple example is given in Figure 5.3.

42 • Further Tools

Figure 5.3: A simple plot using a Maple plot command

Maple Flow also supports 3-D plots. A simple example is given in Figure 5.4.

Figure 5.4: A simple 3-D plot

You can rotate a 3-D plot.
To rotate a plot:
1. Double-click the plot. The 3-D plotting toolbar is shown in the context menu. By default, the rotate tool (enabled.

) is

2. Hold the left mouse button and drag the mouse to re-orient the plot.
3. Release the mouse button when the plot is oriented as desired.
The values of the angles theta, phi, and psi are displayed in the 3-D plotting toolbar to help you orient the plot. You
can also interact directly with the values of these angles.

The orientation is determined by rotating the plot psi degrees around the x-axis, then phi about the (transformed) yaxis, and then theta about the (transformed) z-axis.
To reset the view, use the Reset view icon (). The rotation and zoom of the plot reset to the initial view.

43 • Further Tools

You can resize the plot in the worksheet.
1. Select the plot, as shown in Figure 5.5.
2. Resize the plot. To maintain the aspect ratio, hold Shift while resizing.

Figure 5.5: Resizing a plot

Tip: When the plotting command is long, you may want to line break the command using Shift + Enter. This entersa soft new line, and can be useful for controlling the width of math containers. It also makes it possible for you to resize
the plot narrower, since resizing is naturally limited by the width of the math container.
If you do not want to see the plot command at all, you can hide it as described in Hiding Commands (page 25).

5.6 Matrices
Entering and Using Matrices
Matrix Entry
There are a few ways to enter a Matrix.
The Matrix palette or Matrix command can be used to enter a matrix.
When you use the Matrix palette, shown in Figure 5.6, a template is inserted into the worksheet.

Figure 5.6: Matrix palette

You can then replace the placeholders in the matrix template, using Tab to move between placeholders.

44 • Further Tools

Figure 5.7: Matrix from palette

To add an additional row or column to a matrix, place your cursor in the matrix and right-click. From the context menu,
select one of:• Insert Row Above• Insert Row Below• Insert Column to the Left
• Insert Column to the Right
Similarly, you can remove a row or column from the context menu.
Tip: Triple-click to select the entire matrix.
Indexing into Matrices

If you've made a matrix definition, such as, you can index into the matrix using indexed notation.

For example, to extract the first entry, you enter M[1,1]. This can by entered by hand or selected from the Expression
palette. To enter this from the Expression palette:
1. From the Expression palette, click. This template is inserted in the worksheet.

2. Replace the placeholders, using Tab to move between placeholders.
In Figure 5.6, further examples of matrix indexing are given.

Figure 5.8: Matrix indexing

Indexing into lists, vectors, or arrays works the same way.
Basic Matrix Operations
Operation
Matrix multiplication
Matrix inverse

SyntaxM.N (period)

Transpose

M+ or LinearAlgebra:-Transpose(M)elementwise(expression)

Elementwise operations

M-1 or LinearAlgebra:-MatrixInverse(M)45 • Further Tools

The elementwise function allows you to apply operators and basic functions element-wise over data container(s) suchas matrices, arrays, or lists. For example, if M and N are matrices of the same dimensions, elementwise(3*log(M)*N)
applies this expression to the positional pairwise entries of these matrices.
More information can be found in the help system.
Viewing Large Matrices and Vectors
Matricesand smaller, and vectors with 10 or fewer elements, display in the document. For larger matrices
or vectors, a portion is shown inline.
For example, insert amatrix.

1. In the Matrix palette, specify the dimensions: 30 rows and 30 columns.
2. In the Type drop-down list, select a matrix type, for example, Random.
3. Click Insert Matrix. The command is inserted; evaluate and display the result.

Figure 5.9: Inline Matrix Browsing

Note the output shows ellipses indicating the data continues and the output is scrollable meaning that you can explore
the values directly within the worksheet, using your trackpad or mouse wheel. To view the entire matrix or vector,
double-click the summary placeholder. This launches the Matrix Browser.
Back in the document, the context menu for the matrix has some controls.

46 • Further Tools• To remove the row and column headers, right-click on the matrix and clear the check boxes for Row Header andColumn Header.

Additionally, you can disable the scrollable functionality by selecting Freeze Scrollable Output from the context
menu. This also freezes the Matrix in its current size and position.
Set Displayed Matrix Size
In Figure 5.9, for the matrix, a certain number of rows and columns are displayed. By default, 10 rows and 10 columns
are displayed in output for any matrix. The same rules apply to one-dimensional and multidimensional data stored asarrays.
You can change this setting in the Options dialog.
To set the maximum number of rows and columns displayed:
1. From the toolbar, click the Options icon ().

2. Under the Display tab, specify the desired values under Output matrix size for:• Row limit• Column limit
3. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.

47 • Further Tools

Figure 5.10: Set matrix size

Set Matrix Save Limit
If a worksheet that contains a large matrix is saved and reopened, the data is saved and is scrollable as long as thematrix has 5000 or fewer entries. With larger matrices, you will need to re-execute or re-import the matrix before
scrolling. This limit can be changed in the Options Dialog:
1. From the toolbar, click the Options icon ().

2. Select the General tab.
3. Enter your value for RTable output save limit.
4. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.

Data Import Assistant
The data import assistant makes it easy to import your data into a worksheet. Supported file types include CSV, delimited,
and Excel files, as well as audio files, image files, and graph formats.
To import data:
1. Click on a blank part of the canvas to create a math container.
2. From the Tools menu, select Import Data. The Data Import Assistant opens.
3. Browse to select a file to import.
4. Follow the steps in the assistant. When prompted, specify a variable name to which to assign the imported data.
5. Click done when prompted. A command is inserted into the math container that will import the data.

48 • Further Tools

Figure 5.11: Import data

5.7 Ease of Use Features
Command and argument completion offer an easy way to get your syntax right when working with commands in Maple
Flow.

Command Completion
Maple Flow offers a dialog for command completion. When typing in a math container, Maple Flow suggests commands
and templates that match what you have already entered.
The command completion dialog is initiated by pressing Esc or Ctrl + Space.

Figure 5.12: Command completion window

The command completion lists include command names and templates. If there are any placeholders in your selection,
they appear in a colored font. Replace the placeholders in the template, using Tab to move to the next placeholder.
Automatic Command Completion
In addition, when typing in a math container, Maple Flow offers automatic completions for items that are unambiguous.
When such a suggestion is available, it appears as a yellow annotation. Pressing the Esc or Tab key inserts the suggesteditem.

49 • Further Tools

Argument Completion
Similar in concept and design to command completion, Maple Flow offers automatic completions for arguments inmany useful cases. When such items are available, Maple Flow displays a popup list of suggested completions.

To use argument completion:
1. If only one item is suggested, press Tab to insert the suggested item into your expression.
2. If more than one item is listed, use the arrow keys to select an entry then press Tab. You can alternatively use yourpointer to select an entry from the list.
The argument completion list can include examples for some suggested items. In such a case, if you select that entry,
the example is inserted.

Note: Automatic argument completion is on by default.
To turn off argument completion:
1. From the toolbar, click the Options icon (2. Select the Interface tab.

).

50 • Further Tools

3. Clear the Automatic argument completion check box.
4. Click either Apply to Session or Apply Globally.

5.8 Code Editor
The Code Editor lets you write Maple procedures to use in a Maple Flow canvas. To learn how to write a Maple procedure, read the online Maple Programming Guide:
https://www.maplesoft.com/support/help/Maple/view.aspx?path=ProgrammingGuide/Contents
To view the code editor, click the Code Editor button on the main toolbar, as illustrated in Figure 5.13. Alternatively,from the Edit menu, select Code.

Figure 5.13: Code Editor button on main toolbar

Note: You can only enter proc definitions in the code editor. That is, your code should be in the form:
FirstProc:=proc(...) ... end proc;
NextProc:=proc(...) ... end proc;

To define the procedure, enclose a sequence of statements between proc(...) and end proc statements, and specify theparameter name(s) in the parentheses after the proc statement. For example, a simple definition for a procedure thattakes one parameter and returns the square of the parameter is:
MyProc:=proc(x) x^2; end proc;

5.9 Logging Debugging Information
Maple Flow uses a log file. It always includes some information on the startup routine.
If necessary, you can enable the logging of debugging information into the log file. This information may be needed
if you contact Technical Support.

51 • Further Tools

To enable logging of debugging information:
1. From the toolbar, click the Options icon ().

2. Under the General tab, select Include debugging information in log file.
3. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session and future sessions.
Now, the log file will include information that can be used for troubleshooting.
Note: The log file is located here:• On macOS: ~\Users\username\.maplesoft\maplesoft.log• On Windows: C:\Users\username\.maplesoft\maplesoft.log

6 Printing and Exporting to PDF
6.1 Printing a Maple Flow Document
The following sections describe settings you can control when printing or exporting to PDF.
Whenever you prepare a document for printing or export to PDF, the entire document re-evaluates if needed so everythingreflects the current state.

6.2 Print Extents
Selecting View > Print Extents displays dashed horizontal and vertical lines. These indicate the extents of a printablepage, taking into account the chosen page size, margins and headers/footers. Pages are printing column-by-column.

Figure 6.1: Print extents5253 • Printing and Exporting to PDF

The on-screen positioning and size of math, text, plots and images will be reflected in the printed page or exported
PDF.
Note: If you only want to print the left-most page, under File > Print Settings, select Print single page width. Thisis useful, for example, if you write extra notes to the side of your work. By using print extents and this setting, you canensure those notes do not end up in the printed version of your document.

6.3 Headers/Footers
The Insert > Header Footer menu permits you specify a header and/or footer. This will be seen in the printed pageor exported PDF, but not in the working environment.

Figure 6.2: Inserting Headers and Footers

Headers and footers can be customized, making it easy to create standardized templates. A header or footer can include
date, timestamp, image, document name, page number, and so on. You can draw borders around the header, footer, or
the body of the document.
To create a multi-line header or footer, use a newline character.
• On Windows, use \n• On Mac, use \r
For example, to create a multi-line header in Windows that contains the date and timestamp on different lines:
1. From the Insert menu, select Header Footer...
2. In the Header Footer window, select the Custom Header tab.

54 • Printing and Exporting to PDF

3. In the Left: text field, click.

4. Also, in the Left: text field, after the newly inserted date, type "\n".
5. Click. The Left: text field will look like this:

6. Click OK.
7. Finally, If you open Print Preview, your header should look like this:Note: For headers or footers on the same line, use the spacebar to insert a space between header or footer elements.

Apply a Header or Footer to All Your Documents
To apply the header or footer to all documents:• Select Apply Globally.
To remove the global definition, open the header/footer dialog and select None for both header and footer, and check
Apply Globally.
To edit the global definition, open the header/footer dialog, made the desired edits, and then check Apply Globally.

55 • Printing and Exporting to PDF

Additional Options
To access additional formatting options, click Options

From the Options menu, you can adjust:Start headers on page. Use the option arrow buttons to select on which page you want the headers to begin appearing.
Start page numbers at. Use the option arrow buttons to select the page you want numbering to begin appearing.
Date Format: You can adjust the date format in your header or footer by selecting one of the available options fromthe list.
Date Format Choice
Short

Displayed as

MediumLong
Full

Scale Image. Scale the size of the inserted image as a percentage of the original size.

6.4 Page Setup
The Page Setup menu lets you change the page size, orientation, and margins, for printing.

56 • Printing and Exporting to PDF

Figure 6.3: Page Setup

To specify the page setup for one document:• Use File > Page Setup to specify the settings.
The page layout is saved with the document and remembered when it is reopened.
To set the default page layout:
1. From the toolbar, click the Options icon ().

2. In the Template tab, click Set default page layout. The Page Setup dialog opens. Specify the settings and clickOK.
3. Click Apply to Session to apply for the current Maple Flow session only, or click Apply Globally to apply thesetting to the current session an future sessions.

6.5 Print Preview
The File > Print Preview menu lets you preview the printed page or exported PDF.

6.6 Export to PDF
On Windows:
To export the worksheet to PDF:
1. Select File > Export As.
2. Browse to the desired location and specify a filename. Click Save.

57 • Printing and Exporting to PDF

On Mac:To create a PDF of the worksheet:
1. Select File > Print.
2. Select Save as PDF.
3. Specify a filename. Click Save.

6.7 Printing a Worksheet with Sections
Whether printing or exporting to PDF, if your Maple Flow worksheet has sections, you can select how it is printed.
Select File > Print Settings. Select one of the following:• Print/export document with all sections expanded.
• Print/export document keeping sections exactly as shown on-screen.
If you selected the first option, in addition, specify whether to print the section boundary markers.
For more information on controlling the display of sections, see Controlling the Display of Sections (page 24).

7 Keyboard Shortcuts
Maple Flow provides many keyboard shortcuts for ease of use. These are given in the following tables.
Table 7.1: Keyboard shortcuts for canvas operations
Windows
Canvas operations
With the grid cursor on an empty row: move the grid Enter
cursor, and all content below the grid cursor, downWith the grid cursor on an empty row: move the grid Backspacecursor, and all content below the grid cursor, up
With the grid cursor on an empty row: move all
Deletecontent below the grid cursor up
With the grid cursor on a container: move theCtrl + arrow keys
container
Ctrl + Shift + arrow keys
With the cursor in a container: delete the container Ctrl + Delete
Move to next container
Tab
Move to previous container
Shift + Tab
Cursor to top of canvas (first container)
Ctrl + Home
Cursor to bottom of canvas (last container)
Ctrl + End

Mac
ReturnBackspace
DeleteCommand + arrow keys
Command + Shift + arrow keys
Command + Delete
Tab
Shift + Tab
Command + Home
Command + End

Table 7.2: Keyboard shortcuts for math entry
Windows
Math
Evaluate math and display output*=
Update math container, then continue editing
Ctrl + Enter
Entering an equal sign to mean equality*
Ctrl+ =
Add units to a value or expression
Ctrl + Shift + U
Navigate through expression[←][→][↑][↓]
Move cursor to different level in expression, e.g. out [→]of exponentx/yFraction

Mac=
Command + Return
Command + =Command + Shift + U[←][→][↑][↓][→]
x/y

Inline fraction

x\/y

x\/y

Literal subscript

x__n (two underscores)

x__nExponent
Command or symbol completion

x^n

x^n

Esc, orEsc, orCtrl + SpaceEnter a Greek character**Ctrl + G
Navigate between placeholders in a math expression Tab, or

Toggle between numeric/symbolic mode for mathcontainer
Soft new line
Disable/enable evaluation of the worksheet
Interrupt evaluation

Command + Shift + SpaceCommand + G
Tab, or

Shift + Tab (navigate backwards)
Alt + S

Shift + Tab (navigate backwards)
Ctrl + S

Shift + Enter
Ctrl + E
F6

Shift + Return
Command + E
F6 + Command + . (period)5859 • Keyboard Shortcuts* You can change the behavior of the = key in a math container through the Options > Evaluation dialog. For details,
see Controlling Evaluation (page 18).
Some notes on the evaluation shortcuts on international keyboards are found in the following table.
Table 7.3: International keyboard shortcuts for evaluation

Evaluate math and display output

German keyboard
Shift + 0, for Mac and Windows

Japanese keyboard
Shift + -, for Mac and WindowsEntering an equal sign to mean equality

Shift + Alt + 0, for Windows

Ctrl + Shift + -, for Windows

Command + Shift + 0, for Mac

Command + Shift + -, for Mac** To enter a Greek character, type the indicated Roman letter from the keymap in the following table, then type Ctrl
+ G (Command + G, for Mac) to get the corresponding Greek character.
Table 7.4: Greek Keymap
Type

Lowercase
Greek

Type

a

A

b

B

c

C

d

D

e

E

f

F

g

G

h

H

i

I

j

J

k

K

l

L

m

M

n

N

o

O

p

P

q

Q

r

R

s

S

t

T

u

U

v

V

w

W

UppercaseGreek60 • Keyboard Shortcuts

Type

Lowercase
Greek

Type

x

X

y

Y

z

Z

Uppercase
Greek

Table 7.5: Keyboard shortcuts for text entry

Text
Create a text box
Switch to math entry in a text box
Switch back to text entry

Windows

Mac

Space
Ctrl + R
Ctrl + T

SpaceCommand + R
Command + T

Table 7.6: Keyboard shortcuts for menu operations

File
New
Open
Close worksheet
Save
Save as ...
Print
Page setup
Exit
Edit
Undo
Redo
Find/Replace
Select all
Remove section
Code editor
View
Zoom factor—default
Zoom factor 75%
Zoom factor 100%
Zoom factor 125%
Zoom factor 150%
Zoom factor 200%
Zoom factor 300%
Zoom factor 400%
Zoom in

Zoom out

Windows

Mac

Ctrl + N
Ctrl + O
Ctrl + F4
Ctrl + S
Ctrl + Shift + S
Ctrl + P
Ctrl + Shift + P
Alt + F4

Command + N
Command + O
Command + W
Command + S
Command + Shift + S
Command + P
Command + Shift + P
Command + Q

Ctrl + Z
Ctrl + Y
Ctrl + F
Ctrl + A
Ctrl + Comma
Ctrl + Shift + E

Command + Z
Command + Y
Command + F
Command + A
Command + Shift + Comma
Command + Shift + E

Ctrl + 0
Ctrl + 1
Ctrl + 2
Ctrl + 3
Ctrl + 4
Ctrl + 5
Ctrl + 6
Ctrl + 7
Alt + Plus, orCommand + 0
Command + 1
Command + 2
Command + 3
Command + 4
Command + 5
Command + 6
Command + 7
Control + Shift + =Alt + =
Alt + -

Control + Minus, orControl + Shift + Minus

InsertPage breakFormatCtrl + Enter

Command + Return61 • Keyboard Shortcuts

Bold
ItalicUnderline
Tools
Spellcheck
Help
Maple Flow Help
Help on Context

Windows
Ctrl + B
Ctrl + I
Ctrl + U

MacCommand + B
Command + I
Command + U

F7

F7

F1
F2

F1
F2

Windows
Single-click
Double-click
Triple-click

Mac
Single-click
Double-click
Triple-click

Table 7.7: Mouse bindings

Locate cursor
Select current word, in text container
Select entire matrix, piecewise expression, or
containerdrawings
creating, 26

Index

E

Symbols

editable option, 26
editing, 8
editing units, 16elementwise, 44
entering
math container, 8, 11
text container, 8, 21
entering mathbasics, 15command completion, 15
complex numbers, 15
definition, 11
in a text paragraph, 21
nonexecuting, 18, 19, 21
using =, 11
option to change evaluation keys, 18
using palettes, 15
entering units, 15
evalf, 12evaluation
disable temporarily, 19interrupt, 18
only visible containers, 18
order of, 18
progress bar, 18
using =, 11international keyboard shortcuts, 59
evaluation modes
numeric and symbolic, 12:=, 11align results under definition operator, 25=
for equality, 11
to display results, 11international keyboard shortcuts, 59Aaccuracy, 17
aligncontainers to the left, 9
result on new line, 25
assigningalign results under :=, 25
hide commands and name, 25
value to a name, 11

Bbackground color
for container, 21
bookmarks, 34
bring
to front/back, 10

Ccanvas, 4code editor, 50
command completion, 48
commands
getting help on, 3
complex numbers, 15
context panel, 4, 13
control display of mathhide commands, 25
numeric formatting of result, 13
symbolic or numeric result, 12
control display of resultsalign under :=, 25
control editability of document, 26

Fflip
to front/back, 10
formatsection style, 24
using character formatting, 23
using style sets, 23
functions
Maple, 38

GDgraphing, 41
Greek characters
entering, 59
grid, 8debugginglog file, 50
defining procedures, 50
definition
creating, 11
Digitsfor numerical evaluation, 17

H
help

62

Indexon additional Maple commands, 3
help system, 3hide commands, 25
home page, 1
customize, 6
hyperlinks
inserting, 34

I
i, 15
imagesdrawing on, 26
inserting, 26
import datausing assistant, 47
indexing
into matrices or lists, 44
insertheader or footer, 53
section, 23

K
keyboard shortcuts, 58

Llinking
to a bookmark, 34
to another worksheet, 34
locationgrid cursor, 8M
Maple Flowversus Maple, 2Maple Flow window, 4math containerfor display only, 18
set background color, 21
matrixentering, 43
importing data for, 47
large, 45
operations, 44
random, 45
select entries, 44
set matrix save limit, 47
set visible matrix size, 46
view entries, 45
movingmath container, 8changes evaluation order, 18
text container, 8Nnumeric evaluation, 12
numeric formatting options, 13O
open
in new window, 6
Options
default zoom, 5
display
set number format, 13
evaluate
entire worksheet, 18
evaluation keys, 18
on loading worksheet, 18
only visible containers, 18

Ppackagesusing Maple, 38
palettes, 4, 15, 43
units, 16variables, 41
pastingin math container, 11
PDF
export to, 56
pi, 12plotting, 41
print
set default page layout, 55
settings for sections, 57
single page width only, 52
print preview, 56
printing, 52
programming, 50

Rrandommatrices, 45
rounding
specify decimal places, 13
rtablesize option, 47

Sscientific formatting, 13sectionexpand or collapse, 23
sections, 23
display of, 24
shortcuts
inserting, 34

Indexstatus bar, 18
symbolic evaluation, 12
syntaxdocumentation, 38
for commands, 48

Ttext
formatting, 21
formatting using built-in styles, 23
using character formatting, 23
text container, 21
entering math in, 21
set background color, 21
toolbars, 4
troubleshooting
logging debugging information, 50
turning evaluation off, 19
tutorials, 1Uunits, 15, 38
add custom unit, 40changing units of a result, 39
default units system, 38
dimensional balancing, 40
rescaling, 16Vvariables
manager, 41
vectorlarge, 45
view
print extents, 52
visual indicators, 12, 19, 25, 36

Zzoom
set default, 5