### The Rapid Mathline

With MathCast, all of the “inputting” and “editing” of equations is done through this mechanism. The Rapid Mathline’s main design goal is to be as simple and as logical as possible, while at the same time be powerful enough for advanced editing.
The main disadvantage of the Rapid Mathline is that the equations are displayed in a “calculator-like” row instead of a mathematical representation. Although, this is also its main advantage, since it incorporates an intelligent engine that automatically styles your equations to look as they should, thus allowing you to type-in the equations more rapidly. (The mathematics generated by MathCast, if you notice, is the same as that of most books. This is the standard adopted by the mathematician community.)

#### Operation

To edit an equation:

- In the Edit Screen, select an equation with the mouse or keyboard.
- If the equation isn't empty, then a Mathline presentation can be seen in the Rapid Mathline.
- Click inside the Rapid Mathline with the mouse, or press Enter.
- You can use the keyboard to type-in an equation in Mathline format. Notice that for some keys, pressing them more than once will give you alternate characters. This is called Quick Keys. You can enable/disable this feature by pressing Ctrl+Q.
- Some special characters can be entered through pressing the Ctrl key and another key. This is called Hotkeys.
- You can also use the mouse to select characters from the Lowlist.
- Every available element which can be entered into the Rapid Mathline can also be selected from the Math Menu.
- Copy, cut, paste, and other functions are also operational.

#### Basics

The Rapid Mathline identifies the following elements: numbers, letters, function names, mathematical operators, shortcuts, and markup. All of these elements can be entered individually, except for the markup characters, which require parameters.
Before we go into details about each element, here are some examples:

Mathline Text | Rendered Result
--- | ---
`2a + 3.5b = c` |
`α×β ≠ γ÷δ` |
`x1 +x2+ x3+ …` |
`sin(ax) + cos(bx)` |
`"matrix A:" ░◢A` |
`a² + b^4 = √c` |
`2╱‹a + b›` |
`∑‡0¸100 x^n` |
`∫¦0¸‹t + 100› t² dt` |
`x̅ + y̅ = z̅` |
`lim_‹x→0› ‹sin x›╱x` |

#### Numbers

A number is made up of a series of digits, without spaces between. It may include commas and periods (including a period as the first character).
Examples:
`120`
`10.20`
`1,500`
`5.1.2.3`
`.987`
`10,20,30.12.34,3`

#### Letters

A letter consist of one character: ‘A’ through ‘Z’, ‘a’ through ‘z’, Greek letters, double-struck letters, or special letters.
Examples:
`a`
`T`
`Β`
`Ψ`
`ℝ`
`ℒ`
`℃`
Letters are usually used for conveying identifiers or variables in mathematics.

#### Function Names

Function names are predefined names consisting of a few letters grouped together (without spaces between).
Examples:
`sin`
`Arctan`
`lim`
`det`
Unlike letters, function names do not display in italic text style, but rather as normal text style. If the letters don’t spell-out a function name, the Rapid Mathline will take all the letters individually (as if there is an invisible times between them).

#### Operators

Mathematical Operators are one-character long symbols used in mathematics.
Examples:
`+`
`=`
`∯`
`∡`
`∑`
`≤`

#### Markup

The markup elements are elements that have a special appearance or meaning. They are created with the help of the markup characters.
These are the 20 predefined markup characters: `◢░◟^¦_¯‡"‹›()¸√∜╱⁄⌈⌋`
These characters are different from the other characters (operators and letters) in that they require parameters.

##### Superscripts, Subscripts, Underscripts, and Overscripts

This table summarizes the x-scripts:

Character | Name | Arguments | Syntax | Result
--- | --- | --- | --- | ---
`◟` | subscript | base + arg | `b◟x` |
`^` | supscript | base + arg | `b^x` |
`¦` | subsupscript | base + 2 args | `b¦x¸y` |
`_` | underscript | base + arg | `b_x` |
`¯` | overscript | base + arg | `b¯y` |
`‡` | underoverscript | base +2 args | `b‡x¸y` |

Notice that for subsupscript and underoversript the two parameters are separated by the argument separator character ‘`¸`’.
Note: When you want to add an index to a letter, for example , you don’t need to type `x◟10`, typing `x10` will give you the same result.

##### Fractions

To type-in a fraction, use the ‘`╱`’ character. A fraction requires 2 parameters: a numerator and a denominator. For the input `n╱d`, the rendered result would be .
Note: MathCast supports bevelled fractions (n/d), however at this time it doesn’t display them correctly. You can still use it though for MathML or for future compatibility. It is available through the “slash over” character.

##### Roots

To type-in a square root, use the ‘√’ character, followed by whatever you need in the root. So for `√r` the rendered result would be .
To type-in an n’th-root, use the ‘`∜`’ character. Before it, type the n, and after it, type the root. So `n∜r` would render as .

##### Bold

To specify bold style appearance for your mathematics, use the bold markup character, ‘`◢`’. The syntax is: `◢b`, and the rendered result is: .

##### Text

To add text to your mathematics, use a couple of double-quotes and enter the text between them: `"Sample"` would render as .

##### Spaces

To add a small space, use the space markup character, ‘`░`’.
The syntax is: `a░b`, and the rendered result is: .

##### Blocks and Parentheses

In many equations, you would want to group a few elements together. This is especially useful when working with other markup characters, such as fractions, roots, and scripts. To put a few elements in a block, use the ‘`‹`’and `‘›`’ characters. The Hotkeys for these are: Ctrl+9 and Ctrl+0 or Ctrl+,(coma) and Ctrl+.(dot).
Here are some examples:

Mathline Text | Rendered Result
--- | ---
`‹a + 1000›╱‹b − a²›` |
`√‹a + 100²›` |
`‹du›╱‹dt›` |
`x^‹jω + φ›` |
`|∫xdx|` |
`|‹∫xdx›|` |

Parentheses, like blocks, allow you to group elements together. But unlike blocks, Parentheses are shown in the rendered equation. For example: `(∫xdx)` would render as .
In the Rapid Mathline, you must close all blocks and parentheses.

##### Vector - 2D Matrix

In order to add a two-dimensional matrix (or vector), use the ‘`⌈`’, ‘`⌋`’, and argument separator characters.
For example, `⌈a¸b⌋` will render as .
And to get a vector with parenthasis around it, `(⌈10¸5+4¸20⌋)` will give .
Also notice that the blocks are inferred automatically, you don't need to input `‹5+4›`.

##### Matrix

A matrix, like the vector, requires the ‘`⌈`’, ‘`⌋`’, and argument separator characters.
For example, `⌈ ⌈a¸b⌋⌈c¸d⌋ ⌋` will render as .
The outer ‘`⌈`’ and ‘`⌋`’ tell the Rapid Mathline that we are talking about a matrix. While the internal ‘`⌈`’ and ‘`⌋`’ repressent the rows of the matrix.

#### Shortcuts

Shortcuts are basically a few characters represented by another character.
For example, if you enter `x²` in the Mathline, the squared character is actually a shortcut for `^2`. Thus, when you enter `^2`, the Rapid Mathline automatically places the shortcut ‘`²`’ after you press Enter.
All the overhead operators, such as vector and overline, are also shortcuts.