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Getting Started
Sym is a tool for creating and manipulating symbolic content. By symbolic content, we mean both mathematical expressions and other symbolic content (source code is one example). Almost anything that can be represented as a tree of symbols can potentially be content in Sym. The topics in the Getting Started section of the documentation cover installing Sym and starting to use Sym.
Commands
Commands are used both to construct and manipulate expressions. Typically, single-character keystrokes are used to invoke commands. For example, the "s" keystroke normally runs the Simplify command on the highlighted expression.
The Sign Command
The Sign command lets you manipulate and move minus signs in expressions. Minus signs are manipulated by other commands, for example, the Equivalence command, but the sign command gives more flexibility in controlling where the signs end up making it useful for moving signs around in more complicated expressions. There are two different sign commands. The keystroke for the two Sign commands are the i key and the I key.

Getting Started
Sym is a tool for creating and manipulating symbolic content. By symbolic content, we mean both mathematical expressions and other symbolic content (source code is one example). Almost anything that can be represented as a tree of symbols can potentially be content in Sym. The topics in the Getting Started section of the documentation cover installing Sym and starting to use Sym.
- Installing Sym
  Sym includes a Windows installer. The installation requirements and info about the install destination are listed below.
- Using Sym
  To get started using Sym, you need to understand the basics of how documents and content are created and edited.
- Documents
  Every document has two main components; the document content that you create and the libraries that define the objects and functionality available in the document. Documents will nearly always have a reference to least one library. Without any libraries loaded there would be virtually no functionality available in the document.
- Commands
  Commands are used both to construct and manipulate expressions. Typically, single-character keystrokes are used to invoke commands. For example, the "s" keystroke normally runs the Simplify command on the highlighted expression.
  - Creating and Editing Commands
    Commands allow you to manipulate expressions. Each command defines the function that will be executed when the command is applied to the highlighted expression. Commands typically also have a shortcut key assigned to them.
  - The Result List Pop-up
    The result list pop-up provides a way for the user to select a result when a command returns multiple expressions.
  - Commands Used to Create and Edit Expressions
    The Backspace, Enter, Delete, and Insert keystrokes are all tied to commands so that the action of these keystrokes on expressions can be modified and extended as new libraries are created.
  - The All Command
    The All command displays a list of other commands that can be applied to the highlighted expression. It was created to make it easy to find whatever command you need. Selecting any of the commands shown will apply the command to the highlighted expression. In some cases, a command shown in the list will just generate another list of commands to select from. The keystroke for the All command is the "a" key.
  - The Combine Command
    The Combine command is used most often when working on expressions that contain a large number of parameters. It can isolate a few parameters from the rest of the expression so that it's easier to manipulate the isolated terms. The terms that are combined are place inside of the Parentheses object.
  - The Convert Command
    The Convert command is used mainly when you are editing expressions. Unlike the Equivalence command, the results generated by the Convert command are usually not mathematically equal to the starting expression. The keystroke for the Convert command is the "c" key.
  - The Division Command
    The Division command is used to do manipulations on the Div object. The keystroke for the Division command is "d".
  - The Equivalence Command
    The Equivalence command provides access to forms of an expression that are equivalent to the highlighted term. This command typically shows a result list with more than one option. The keystroke for the Equivalence command is the "q" key (the "e" key is used for the Expand command).
  - The Evaluate Command
    The Evaluate command is used to do numeric evaluation of expressions. It is used on expressions that can be evaluated to a single numeric value. It can also act on Boolean expressions like "True & False" and on certain relationships between types. The keystroke for the Evaluate command is the "a" key.
  - The Execute Command
    The Execute command executes the highlighted expression in a fashion similar to what would happen if the expression were a clause inside of a function that was being executed. If the Calc.eql library is loaded, then the Execute command also includes things like executing derivatives and integrals. The keystroke for the Execute command is the "x" key.
  - The Expand Command
    The Expand command is used to change an expression to an expanded form. For example, Expand applied to the expression x*(y + 1) give x* y + x. This command typically just modifies the highlighted term. The keystroke for the Expand command is the "e" key.
  - The Factor and FactorAll Command
    The Factor command can either factor only the highlighted term or factor out the highlighted term from any of its parent terms. The Factor command is primarily used with algebraic expressions. The keystroke for the Factor command is the "f" key. There is also a FactorAll command that acts on all terms in the expression rather than only those including the term being factored. The keystroke of the FactorAll command is the "F" key.
  - The Increment and Decrement Commands
    The Increment and Decrement commands are used primarily with numbers and units. The keystroke for the Increment command is the Alt + Up arrow key. The keystroke for the Decrement command is the Alt + Down arrow key.
  - The Left and Right Commands
    The Left and Right commands are used to reorder terms in algebraic expressions involving addition, subtraction, and multiplication. This command normally modifies one of the parent expressions of the highlighted term. The Left and Right commands will also reorder terms in other commutative monoids. For expressions involving addition and subtraction, the RightIn and LeftIn commands will move terms in and out of parenthesized terms. The shortcuts for the Left and Right commands are the "l" and "r" keys, respectively. For the LeftIn and RightIn commands, the shortcuts are the "L" and "R" keys.
  - The Move Command
    The primary purpose of the Move command is to provide a way to move terms in algebraic expressions back and forth across top level expressions that are either equalities and inequalities. This command normally modifies one of the parent terms of the highlight. The keystroke for the Move command is the "m" key.
  - The Question Command
    The Question command is designed to make it faster and easier to construct some kinds of expressions. For example, if you are creating or editing a Graph expression, the question command can be used to pop up lists of objects that can be inserted in the current location. If there is a single empty box in the parameter of the Graph object and you use the Question command, the list that is shown will contain all of the components of a graph. The keystroke for the Question command is the "?" character.
  - The Rendering Options Command
    The RenderingOptions command is used to switch between renderings of an expression in cases where more than one rendering is used in the same notation. An example is the derivative were it's common to use both d/dx(f) and df/dx. The keystroke for the RenderingOptions command is the "F3" key.
  - The Sign Command
    The Sign command lets you manipulate and move minus signs in expressions. Minus signs are manipulated by other commands, for example, the Equivalence command, but the sign command gives more flexibility in controlling where the signs end up making it useful for moving signs around in more complicated expressions. There are two different sign commands. The keystroke for the two Sign commands are the i key and the I key.
  - The Simplify Command
    The Simplify command acts on a wide variety of expressions. It contains functionality that reduces expressions to a simpler form. The keystroke for the Simplify command is the "s" key.
  - The Solve Command
    The Solve command is designed to manipulate an equation into a form that presents a solution. Typically, a variable in an equality or inequality is highlighted and the solve command tries to isolate that variable on the left hand side of the equation.
  - The Substitute Command
    The Substitute commnand provides a way to substitute one expression for another in a target expression. A simple example would be substituting x = y + 1 into the expression x - 2y = 3 to get (y + 1) - 2y = 3. Using this command is a two step process where we first select the expression that defines the substitution (normally an equality) and put it on the clipboard using the normal Copy functionality, then highlight the target expression and apply the Substitute command. The keystroke for the Substitute command that applies this substitution to the target expression is "b".
  - Default commands
    Some of the commands are created by default because we need these commands to exist even if they aren't defined in any of the referenced libraries. Creating these commands allows the appropriate default behavior to exist for these keystrokes even when no libraries are referenced.

The Sign Command

The Sign command lets you manipulate and move minus signs in expressions. Minus signs are manipulated by other commands, for example, the Equivalence command, but the sign command gives more flexibility in controlling where the signs end up making it useful for moving signs around in more complicated expressions. There are two different sign commands. The keystroke for the two Sign commands are the i key and the I key.

The first Sign command does the most common sign manipulatiions. For example, highlighting

x - (1 - y)

and pressing the i key results in

x + (y - 1)

The second sign command (its keystroke is capital I) is available because it wouldn't be practical to list every possible way to move a minus sign in a long expression.. Using the second Sign command introduces a special object, the MinusOne object, that can be moved around and simplified to get the signs where you want them. Unlike the normal minus sign, the MinusOne object doesn't automatically get combined with other objects making it easier to put the signs were you want them.

The normal usage of the second sign command involves initially using this command to convert signs to MinusOne objects, moving those objects around (and possibly simplifying) and finally using this sign command again to convert the MinusOne objects back into normal subtractions and minus signs.

A few examples will make this idea clear. Suppose you are starting with the expression

and want to change this to

One way to do this would be to use the Sign command 2, highlight each MinusOne object an use the Factor command, simplify the whole expression, then use the Sign command 2 again to put the expression in its final form

Once you have changed the expression to contain MinusOne objects, you can move these objects around using other commands (like Expand, Factor, Simplify and so on) just like you would for any other term in an expression.

Note that the MinusOne object simplifies in the same way that an ordinary (-1) would. MinusOne times itself is 1 and powers of MinusOne simplify to either MinusOne or 1 depending on whether the power is an odd or even integer.