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Components of the Sym application
The three main components of the Sym application are the content, the tools used to edit and manage the content and the libraries that provide the objects and functionality that are used to create and edit expressions.
Libraries
There are a number of libraries that are available online that can be used with Sym documents.
The Math Library
The Math library defines basic algebraic objects for things like addition, multiplication, powers, roots, and so on. It extends the commonly used commands to implement functionality like the simplification of algebraic expressions.

Components of the Sym application
The three main components of the Sym application are the content, the tools used to edit and manage the content and the libraries that provide the objects and functionality that are used to create and edit expressions.
- Content
  Content windows include Document Modules, Object Modules and Unit Test Modules. With the exception of the Properties windows which are attached to modules, all of the windows in the Sym application can be dragged and docked in a variety of locations to provide a way to customize the layout of the main application window.
- Tools
  In addition to the content of the application there are several tools available to assist you in creating and managing the content of a document, like the Document Explorer, Object Browser and Unit Test Runner.
- Libraries
  There are a number of libraries that are available online that can be used with Sym documents.
  - The Basics Library
    The Basics library contains the foundations needed for most other libraries. It defines a number of objects that provide basic functionality including the core objects used in the Sym programming language, the LambdaAbstraction, basic Boolean objects and so on.
  - The Core Library
    The Core library is built on top of the Basics library and contains foundations needed for most other libraries. It defines the commonly used commands like Simplify, Equivalence, etc.
  - The Math Library
    The Math library defines basic algebraic objects for things like addition, multiplication, powers, roots, and so on. It extends the commonly used commands to implement functionality like the simplification of algebraic expressions.
  - The Trig Library
    The Trig library defines the standard trig functions, their inverse functions, the hyperbolic trig functions and their inverse functions. It extends the commonly used commands to include functionality to manipulate these objects.
  - The Calc Library
    The Calc library defines the Limit, Derivative, and Integral objects along with variations on these objects and several supporting objects. It extends commands like Simplify, Expand, etc. to act on the new objects. Integrals and derivatives are calculated using the Execute command.
  - The TextFormatting Library
    The TextFormatting library defines a number of objects, commands, and functions that are used to format text.
- Dialogs

The Math Library

The Math library defines basic algebraic objects for things like addition, multiplication, powers, roots, and so on. It extends the commonly used commands to implement functionality like the simplification of algebraic expressions.

The Math library defines:

Most of the commonly used commands
Scientific notation
Several types used in algebraic objects
Inequality objects
Functionality to manipulate algebraic expressions, including functionality in the Division, Equivalence, Expand, Factor, Left and Right, Move, Sign, Simplify and Solve commands.

See the SymCommands example file for more information and examples.