README: included example.php & improved instructions

Makefile

@@ -16,7 +16,7 @@ ci: phplint tester ## Runs complete CI suite
 .PHONY: phplint
 phplint: install
 	@echo '> PHP linter ...'
-	@php vendor/bin/parallel-lint Simplex/ tests/ example.php --colors
+	@php vendor/bin/parallel-lint Simplex/ tests/ --colors
 	@echo ''
 
 .PHONY: tester

README.md

@@ -1,18 +1,99 @@
-Simplex Calculator
-==================
+# Simplex Calculator
 
-Live demo: http://simplex.tode.cz
+## About
 
-This is a simple PHP tool for linear programming problems solving using dual simplex algorithm.
+PHP library for solving linear programming problems using dual simplex algorithm.
 
-It can detect none, one and only and more optimal solutions to any linear problem you tell it to solve.
+**NOTE:** Basis cycling detection is not implemented.
 
-However, the only thing that has been left unimplemented is basis cycling detection. Feel free to post pull requests ;-)
 
-Enjoy.
+## Installation
 
+The recommended way is to use [Composer](https://getcomposer.org/):
 
-Conventions
------------
+```bash
+composer require uestla/simplex-calculator
+```
 
-Please name your variables as **x<n>** where *<n>* is a natural number (see [example.php](https://github.com/uestla/Simplex-Calculator/blob/master/example.php) for details).
+You can also download the latest [release](https://github.com/uestla/Simplex-Calculator/tags) as a ZIP file.
+
+
+## Conventions
+
+Please name all your input variables as `x<n>` where `<n>` is a natural number (see [example below](#defining-and-solving-simplex-tasks) for details).
+
+
+## Usage
+
+### Loading library
+
+```php
+// using Composer
+require_once __DIR__ . '/vendor/autoload.php';
+
+// using manual download
+require_once __DIR__ . '/Simplex/simplex.php';
+```
+
+### Defining and solving simplex tasks
+
+```php
+// define task: Maximize x1 + 2x2
+$task = new Simplex\Task(new Simplex\Func(array(
+	'x1' => 1,
+	'x2' => 2,
+)));
+
+// add constraints
+
+// 3x1 + 2x2 <= 24
+$task->addRestriction(new Simplex\Restriction(array(
+	'x1' => 3,
+	'x2' => 2,
+
+), Simplex\Restriction::TYPE_LOE, 24));
+
+// -2x1 - 4x2 >= -32
+$task->addRestriction(new Simplex\Restriction(array(
+	'x1' => -2,
+	'x2' => -4,
+
+), Simplex\Restriction::TYPE_GOE, -32));
+
+// create solver
+$solver = new Simplex\Solver($task);
+
+// get solutions
+$solution = $solver->getSolution(); // array('x1' => 0, 'x2' => 8, 'x3' => 8, 'x4' => 0)
+$alternativeSolutions = $solver->getAlternativeSolutions(); // array(array('x1' => 4, 'x2' => 6, 'x3' => 0, 'x4' => 0))
+
+// get optimal value
+$optimum = $solver->getSolutionValue($solution); // 16
+
+// print solutions
+$printer = new Simplex\Printer;
+$printer->printSolution($solver);
+
+// or print the whole solution process
+$printer->printSolver($solver);
+```
+
+
+### Solutions
+
+`$solver->getSolutions()` returns primary optimal solution. The value can be of 3 types:
+
+- `array` - vector with optimal coefficients to each input variable
+- `false` - optimal solution does not exist
+- `null` - not enough steps to find solution
+
+By default, solver stops the calculation after 16 simplex tables. You can increase the maximum steps limit with the second parameter:
+
+```php
+$solver = new Simplex\Solver($task, 32);
+```
+
+`$solver->getAlternativeSolutions()` returns array of other optimal solutions if any have been found. It may return:
+
+- `array` - array of vectors with alternative optimal solutions
+- `null` - no alternative optimal solution found