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Equation Operating System: Solve equations with multiple variables

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Version License PHP version Categories  
eos 3.2.1GNU Lesser Genera...5.3Graphics, Math
Description Author  

This class solves equations with multiple variables.

It does not resort to the PHP eval() function to help prevent security risks of using malicious expression values for instance with a calculator that takes expressions defined by the users.

It comes with a sub-class that can produce graphic charts plotting the curve defined by the equation expression withing a given range of x and y values. The generate chart graphics can be outputted in the PNG or JPEG formats using the GD library.

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Solving equations can have many applications, like for instance, drawing charts that represent the curves defined by assigning values of given ranges to the variables of the equations.

The PHP eval() function can be used to dynamically evaluate the expressions defined by an equation. However, it may be dangerous to evaluate an arbitrary expression provided by an user, as it may contain malicious code.

This class provides an alternative solution that consists in a full expressions parser and evaluator that only supports a limited set of operations that do not represent a security risk when the operations are evaluated.

Manuel Lemos
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Name: Jon Lawrence <contact>
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EOS

Composer Usage

Latest Stable Version Total Downloads License

Add the dependency:

"require": {
    "jlawrence/eos": "3.*"
}

$ composer update and you're done.

Equation Operating System

jlawrence\eos\

This class makes it incredibly easy to use and parse/solve equations in your own applications. __NOTE__ ALL of the functions within these classes are static. It is also important to note that these classes throw exceptions if running in to errors, please read the beginning of the Math.php file for the defines of the exceptions thrown. Exceptions includes a descriptive message of the error encountered and within Parser will also typically include the full equation used.

Parser

This class has one important function, Parser::solve() which does all the legwork, so we'll start there and end with examples.

use jlawrence\eos\Parser;

solve($infix, $variables)

To use this function:

$value = Parser::solve($eq, $vars);

_$infix_

Is simply a standard equation with variable support.

Example Equations:

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

The parser has good implied multiplication, for everything but allowed functions. Allowed functions require an explicit 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.

_$variables_

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:

5x^y

If this is called by:

Parser::solveIF('5x^y', 2);

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

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

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

jlawrence\eos\Graph

To use:

use jlawrence\eos\Graph;

This is the fun class that can create graphs. The image will default to 640x480, to initialize a different size use:

Graph::init($width, $height);

The $width and $height are the values used for the image size.

graph($eq, $xLow, $xHigh, [$xStep, $xyGrid, $yGuess, ...])

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. Set to null/false to use the smart xStep feature within the graph class.
  • $xyGrid = false Show x/y gridlines on the graph. Defaults to false. Each grid line is set at an integer, with a max of 30 lines, so it will calculate the stepping for it. When the grid is show, the lines are labeled along the top and left side of the image.
  • $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 $yHigh.
  • $yLow = null Lower bound for y. Will be reset if a lower value for y is found if $yGuess is true.
  • $yHigh = null Upper bound for y. Will be reset if a larger y value is found if $yGuess is true.

If you don't want the axis' labeled with their numbers, you can turn off the default behavior with:

Graph::$labelAxis = false;

TODO:

  • Allow user-defined colors for all aspects of the graph.

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();

It would look like: Sin(x)

  Graphing calcExternal page  
  Files folder image Files  
File Role Description
Files folder imagesrc (7 files)
Accessible without login Plain text file README.md Doc. Description of class functionality and use cases
Accessible without login Plain text file composer.json Data Auxiliary data
Accessible without login Plain text file index.php Example Example usage of graphing function

  Files folder image Files  /  src  
File Role Description
  Plain text file AdvancedFunctions.php Class Class source
  Plain text file Graph.php Class Class source
  Plain text file Math.php Class Class source
  Plain text file Matrix.php Class Class source
  Plain text file Parser.php Class Class source
  Plain text file Stack.php Class Class source
  Plain text file Trig.php Class Class source

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