Theme 3. Mathematical modeling. Computer Mathematics Systems

5. The system of symbolic algebra Maple

The Maple system was created by a group of symbolic calculations organized by Gonne in 1980 at Waterloo University, Canada. The price of Maple 18 is about $ 3000.

Maple - this Computer Algebraic System (CAS, C . A . S . - Computer Algebra System ), which means its action under the laws of algebra in the study sections Calculations, Differential Equations and Linear Algebra and others.

The system absorbed most of the mathematical functions and rules of their transformations, which are in mathematics. Maple is used to solving the problems of aerodynamics, field theory, thermal conductivity, theoretical mechanics, etc.

The Maple core is used in MathCAD, MatLAB systems. The latest version is Maple 2018.

The Maple system combines:

• powerful programming language (is the language of interactive interaction with the system);
• editor for preparing and editing documents and programs;
• modern multi-window user interface;
• powerful reference system with many thousands of examples;
• the core of the algorithms and rules for the transformation of mathematical expressions;
• software close and character processors;
• library of built-in functions (more than 3000 for Maple 6) and more.

Maple is a powerful programming language based on three languages:

• the input - which is used for the task questions (input data for their processing). This language is the interpretative type and has a large number of definite mathematical and graphical functions.
• Implementation - Se- terms. In this language, the core of the system is prepared.
• programming - Maple-language. This language has traditional means for solving typical programming tasks based on the principles of a structured approach: loops, conditional and unconditional transitions, logical operators, procedures, etc.

Most of the library functions are prepared in Maple-language, which allows users to complete or modify them.

System interface and work in dialog mode

The Maple system has a standard graphical user interface for programs running Windows operating systems.

Document files include the full text of the program, computational results, graphics information, etc.

A file is a program that is written in an intermediate programming language of the system.

When the program is downloaded, a window is displayed on the monitor screen. In the upper part, directly under the title of the window, is the main menu of the system, whose type (its commands) varies depending on the context: if a graphic object is highlighted on the worksheet, the menu contains commands for working with graphics.

Below the main menu is the main toolbar with a number of buttons that duplicate the most frequently used commands in the main menu.

Directly under the toolbar is a context toolbar, whose type depends on which area of the worksheet is located cursor and that in this area is displayed.

Most of the interface window is occupied by a workspace where worksheets are placed, where commands are entered and the results of their execution are displayed.

At the bottom of the window, there is a status bar that displays some parameters of the Maple system, as well as brief information about the selected menu command or toolbar buttons.

Work in dialog mode

The worksheet consists of an input area and an output area.

Dialog with Maple system occurs in question mode: the user enters the command and pressing [ Enter ] transfers them to the kernel of the Maple system.

The result of the team's operation is displayed in the output field.

To enter a formula in a standard mathematical form, you must execute the Insert - Math Input command. In this case, the input field will display command in the form of Maple syntax, and in the output field, the same command will be displayed in the mathematical notation.

Writing text comments is a mode in which any information is understood as text (not fulfilling).

To insert a text comment, follow the Insert - Text command or click the button on the main toolbar or F 5.

In Maple 18, a button that duplicates the command Edit - Execute - Worksheet is entered on the toolbar.

Main elements of Maple syntax :

• / Flashing inclining risk - marker input formula.
• | | Flashing vertical risk is a text input marker.
• ; The sign of the end of the expression with the output of the result of calculations on the screen.
• : A sign of fixation of the end of the expression, which prevents the output of the result on the screen.
• : = Assignment operator (for example, x: = 4 ).
• = Equality operator for equations and logical conditions (for example, a = b ), indicating areas of change of variables (for example, i = 1 .. 5) and parameter values - options in functions and commands (for example, color = black ).

Moving a command to a new line (without execution) is performed by pressing the [ Shift + Enter ] key combination.

All operators introduced in this way form one group and are executed successively by pressing the [ Enter ] key once.

To insert a new line before the cursor is ([ Ctrl + Shift + K ]) and, accordingly, ([ Ctrl + Shift + J ]) to insert a new line after the cursor.

Basic editing operations are in the main menu item Edit.

• Delete Paragraph or Ctrl + Del - erase the selected objects.
• Find ... or Ctrl + F 5 - find the specified text or mathematical string.
• Input Mode or F 5 - Enable / Disable Text Input.

Maple worksheets are stored in files with the extension mw.

It is possible to save the worksheet in other file formats by entering the Save As command in the dialog as the appropriate format, or use the Export As substitution commands :

• Plain Text. txt is a plain text file.
• Maple Text. txt is a text format of maple.
• HTM .html is an HTML format .
• Maple explorer tex is a format for Maple (allows you to view Maple files ).
• RTF. RTF - format RTF (worksheets pasting into documents MS Word while maintaining the color palette).