This class makes it incredibly easy to use and parse/solve equations in your own applications. It includes a graph generator to turn an equation with a variable in to a y=x graph, with the capability to calculate the upper and lower y-bounds. NOTE NONE of the functions within these two classes are static, any example that looks like a static function call is representational of the class being used, but should be initialized and assigned to a variable first. It is also important to note that these classes throw exceptions if running in to errors, please read the beginning of the eos.class.php file for the defines of the exceptions thrown. Exceptions includes a descriptive message of the error encountered and within eqEOS will also typically include the full equation used.

This class has one important function, eqEOS::solveIF() which does all the legwork, so we'll start there and end with examples.
To initialize this class, use:

$eos = new eqEOS();

To use this function:

$value = $eos->solveIF($eq, $vars);

Is simply a standard equation with variable support. Variables have two forms, one is native to PHP programmers already, prefixed with '$'. The other way to declare a variable is with '&' and is included for backward compatibility for with the initial version from 2005.
Example Equations:

2(4$x)
2(4&x)
5+ ((1+2)*4) +3
5+4(1+2)+3
10*sin($x)
10*cos($x)

The first two pairs shown are exactly the same. The parser has good implied multiplication, for everything but allowed functions. Allowed functions require an implicit operator on either/both sides to work properly, I hope to change that in the next revision; but for now, note that it will not work as you would expect.
For example:

5sin(1.5707963267) = 51
5*sin(1.5707963267) = 5
sin(1.5707963267)5 = 15

The reason is because there is no implied multiplication being applied, the result of sin(1.5707963267) = 1 is being concatenated with the number 5, giving incredibly odd results if you are not expecting it.

The variables are fairly simple to understand. If it contains a scalar (ie a non-array value) every variable within the equation will be replaced with that number. If it contains an array, there will be a by-variable replacement - note that the array MUST be in the format of 'variable' => value
Such as:

array(
    'x' => 2,
    'y' => 3
)

Given the equation:

5$x^$y

If this is called by:

eqEOS::solveIF('5$x^$y', 2)

It will equal '20', as every variable is replaced by 2. However, if called like:

eqEOS::solveIF('5$x^$y', array(
                            'x' => 2,
                            'y' => 3);

You will get the result of '40' as it would equate to 5*2^3, as expected.

This is the fun class that can create graphs. It extends eqEOS.
To initialize use:

$graph = new eqGraph($width, $height);

The $width and $height are the values used for the image size, defaulting to a 640x480 image size if initialized with $graph = new eqGraph();

This method will generate the graph for the equation ($eq) with a min and max x range that it will parse through. All Variables explained:

• $eq The Standard Equation to use. Must have a variable in it. (ie $x)
• $xLow The starting point for the calculations - the left side of the graph.
• $xHigh The last point calculated for the variable - the right side of the graph.
• $xStep Stepping point for the variable. Suggested not to use a value less than .01. This is the precision of the graph.
• $xyGrid = false Show x/y gridlines on the graph. Defaults to false. Each grid line is set at every integer (ie 1,2,3,...100). If working with small ranges, it is suggested to turn this on.
• $yGuess = true Guess the Lower and Upper y-bounds (The bottom and top of the image respectively.) This will set the the bounds to the lowest y value encountered for the $yLow, and the largest y value for $yHight.
• $yLow = false Lower bound for y, will be reset if a lower value for y is found.
• $yHigh = false Upper bound for y, will be reset if a larger y value is found.

TODO:

• Add x and y labels
• Smart grid spacing calculations so can be effective with large ranges.
• Smart (default) $xStep calcuations based on image size and ranges.

To set up a graph with a 21x21 window (ie -10 to 10) for the equation sin($x) and output as PNG, would use as:

$graph->graph('sin($x)', -10, 10, 0.01, true, false, -10, 10);
$graph->outPNG();