Example usage

A number of kinds of problems may be solved. Here they are presented in order of increasing difficulty. Spend time working with variations of each example until you are comfortable solving such problems. Remember that throughout these exercises, your aim should be to become familiar enough that typing each command feels intuitive.

Simple calculator

The program can be used as a simple calculator. For example, execute
    'ae'
which tells the program you want to add a new equation,
    '3+3'
specifies the equation,
    '<Enter>'
This tells the program that you have finished entering the equation and to change back to normal mode.
    '<Enter>'.
This duplicates the equation so that when it is evaluated and replaced, an original version of the problem is kept for reference.
    '='.
This '=' command then evaluates the equation.

In order to clearly distinguish between normal mode and when the equation is being entered, the mode is displayed in the bottom left corner and the string of text being entered is displayed at the bottom centre of the screen.

The commands run together with the calculation, it is clear from the program's user interface when it accepts a branch, and when it is waiting for the next command. This creates a new equation using the 'ae' command. The equation is set to '3+3' and is evaluated using the '=' command. This results in a single integer, 6.

Another, more elaborate example involves finding the angle in a triangle in which the opposite side is known to be 13.4 meters and the adjacent side length is 12.2 meters. This is solved by typing
    'ae'
    'atan(13.4/12.2)'
    '<Enter>'
    '<Enter>'
    '='.
(Ignore new lines and single quotes, this is simply to break up commands for readability This again creates a new equation using the add-equation command, 'ae'. It then accepts the branch 'atan(13.4/12.2)'. After pressing '=', the program then calculates the corresponding value and it is replaced with the corresponding result.

Moving around equations

Generally the program is most useful to add and manipulate equations A simple pair of example equations are Newton's second law,
     F=m*a
and final velocity
     v=u+a*t,
from initial velocity, u, acceleration, a, and time, t. These may be added by the add-equation command 'ae' as before.

Generally when editing equations, it is necessary to move around and explore the equations. The 'j' and 'k' commands move to the next and previous equation. The currently selected equation is always highlighted in red.

Rather than simply act on entire equations, it is often more interesting to edit relative to a particular argument. Specific sub-branches of the equation may be highlighted using the 'i' or 'o' commands move into the first or last argument of the current function. (If you are currently selecting a token then nothing will happen).

Practice moving through the equation to specific locations before moving back out to the parent functions using the '<Space>' command. Additionally, to move to the left or right sibling, use the 'h' or 'l' commands.

Algebra

The program can also be used to perform algebra. For example, Newton's law (above) can be solved for acceleration which can then be substituted into the velocity equation. Dividing both sides of the first equation by mass, m, this becomes
     F/m=a
which can be added below the previous equations with the commands
which can be substituted into the second equation as
     'ae'
     'a=F/m'
     '<Enter>'.

Having found a resulting expression for acceleration, this can be substituted into the velocity equation above. By adding equations and simplifying the results, this becomes
     v=u+(F/m)*t
     v=u+F*t/m.