Updates to 3rd party libraries

Add Dockerfile and specific docker-php.ini

inc/vendor/markbaker/complex/README.md

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+PHPComplex
+==========
+
+---
+
+PHP Class for handling Complex numbers
+
+Master: [![Build Status](https://travis-ci.org/MarkBaker/PHPComplex.png?branch=master)](http://travis-ci.org/MarkBaker/PHPComplex)
+
+Develop: [![Build Status](https://travis-ci.org/MarkBaker/PHPComplex.png?branch=develop)](http://travis-ci.org/MarkBaker/PHPComplex)
+
+
+---
+
+The library currently provides the following operations:
+
+ - addition
+ - subtraction
+ - multiplication
+ - division
+    - division by
+    - division into
+
+together with functions for 
+
+ - theta (polar theta angle)
+ - rho (polar distance/radius)
+ - conjugate
+ * negative
+ - inverse (1 / complex)
+ - cos (cosine)
+ - acos (inverse cosine)
+ - cosh (hyperbolic cosine)
+ - acosh (inverse hyperbolic cosine)
+ - sin (sine)
+ - asin (inverse sine)
+ - sinh (hyperbolic sine)
+ - asinh (inverse hyperbolic sine)
+ - sec (secant)
+ - asec (inverse secant)
+ - sech (hyperbolic secant)
+ - asech (inverse hyperbolic secant)
+ - csc (cosecant)
+ - acsc (inverse cosecant)
+ - csch (hyperbolic secant)
+ - acsch (inverse hyperbolic secant)
+ - tan (tangent)
+ - atan (inverse tangent)
+ - tanh (hyperbolic tangent)
+ - atanh (inverse hyperbolic tangent)
+ - cot (cotangent)
+ - acot (inverse cotangent)
+ - coth (hyperbolic cotangent)
+ - acoth (inverse hyperbolic cotangent)
+ - sqrt (square root)
+ - exp (exponential)
+ - ln (natural log)
+ - log10 (base-10 log)
+ - log2 (base-2 log)
+ - pow (raised to the power of a real number)
+ 
+ 
+---
+
+# Usage
+
+To create a new complex object, you can provide either the real, imaginary and suffix parts as individual values, or as an array of values passed passed to the constructor; or a string representing the value. e.g
+
+```
+$real = 1.23;
+$imaginary = -4.56;
+$suffix = 'i';
+
+$complexObject = new Complex\Complex($real, $imaginary, $suffix);
+```
+or
+```
+$real = 1.23;
+$imaginary = -4.56;
+$suffix = 'i';
+
+$arguments = [$real, $imaginary, $suffix];
+
+$complexObject = new Complex\Complex($arguments);
+```
+or
+```
+$complexString = '1.23-4.56i';
+
+$complexObject = new Complex\Complex($complexString);
+```
+
+Complex objects are immutable: whenever you call a method or pass a complex value to a function that returns a complex value, a new Complex object will be returned, and the original will remain unchanged.
+This also allows you to chain multiple methods as you would for a fluent interface (as long as they are methods that will return a Complex result).
+
+## Performing Mathematical Operations
+
+To perform mathematical operations with Complex values, you can call the appropriate method against a complex value, passing other values as arguments
+
+```
+$complexString1 = '1.23-4.56i';
+$complexString2 = '2.34+5.67i';
+
+$complexObject = new Complex\Complex($complexString1);
+echo $complexObject->add($complexString2);
+```
+or pass all values to the appropriate function
+```
+$complexString1 = '1.23-4.56i';
+$complexString2 = '2.34+5.67i';
+
+echo Complex\add($complexString1, $complexString2);
+```
+If you want to perform the same operation against multiple values (e.g. to add three or more complex numbers), then you can pass multiple arguments to any of the operations.
+
+You can pass these arguments as Complex objects, or as an array or string that will parse to a complex object.
+
+## Using functions
+
+When calling any of the available functions for a complex value, you can either call the relevant method for the Complex object
+```
+$complexString = '1.23-4.56i';
+
+$complexObject = new Complex\Complex($complexString);
+echo $complexObject->sinh();
+```
+or you can call the function as you would in procedural code, passing the Complex object as an argument 
+```
+$complexString = '1.23-4.56i';
+
+$complexObject = new Complex\Complex($complexString);
+echo Complex\sinh($complexObject);
+```
+When called procedurally using the function, you can pass in the argument as a Complex object, or as an array or string that will parse to a complex object.
+```
+$complexString = '1.23-4.56i';
+
+echo Complex\sinh($complexString);
+```
+
+In the case of the `pow()` function (the only implemented function that requires an additional argument) you need to pass both arguments when calling the function procedurally
+
+```
+$complexString = '1.23-4.56i';
+
+$complexObject = new Complex\Complex($complexString);
+echo Complex\pow($complexObject, 2);
+```
+or pass the additional argument when calling the method
+```
+$complexString = '1.23-4.56i';
+
+$complexObject = new Complex\Complex($complexString);
+echo $complexObject->pow(2);
+```

inc/vendor/markbaker/complex/classes/Autoloader.php

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+<?php
+
+namespace Complex;
+
+/**
+ *
+ * Autoloader for Complex classes
+ *
+ * @package Complex
+ * @copyright  Copyright (c) 2014 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ */
+class Autoloader
+{
+    /**
+     * Register the Autoloader with SPL
+     *
+     */
+    public static function Register()
+    {
+        if (function_exists('__autoload')) {
+            //    Register any existing autoloader function with SPL, so we don't get any clashes
+            spl_autoload_register('__autoload');
+        }
+        //    Register ourselves with SPL
+        return spl_autoload_register(['Complex\Autoloader', 'Load']);
+    }
+
+
+    /**
+     * Autoload a class identified by name
+     *
+     * @param    string    $pClassName    Name of the object to load
+     */
+    public static function Load($pClassName)
+    {
+        if ((class_exists($pClassName, false)) || (strpos($pClassName, 'Complex\\') !== 0)) {
+            // Either already loaded, or not a Complex class request
+            return false;
+        }
+
+        $pClassFilePath = __DIR__ . DIRECTORY_SEPARATOR .
+                          'src' . DIRECTORY_SEPARATOR .
+                          str_replace('Complex\\', '', $pClassName) .
+                          '.php';
+
+        if ((file_exists($pClassFilePath) === false) || (is_readable($pClassFilePath) === false)) {
+            // Can't load
+            return false;
+        }
+        require($pClassFilePath);
+    }
+}

inc/vendor/markbaker/complex/classes/Bootstrap.php

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+<?php
+
+include_once __DIR__ . '/Autoloader.php';
+
+\Complex\Autoloader::Register();
+
+
+abstract class FilesystemRegexFilter extends RecursiveRegexIterator
+{
+    protected $regex;
+    public function __construct(RecursiveIterator $it, $regex)
+    {
+        $this->regex = $regex;
+        parent::__construct($it, $regex);
+    }
+}
+
+class FilenameFilter extends FilesystemRegexFilter
+{
+    // Filter files against the regex
+    public function accept()
+    {
+        return (!$this->isFile() || preg_match($this->regex, $this->getFilename()));
+    }
+}
+
+
+$srcFolder = __DIR__ . DIRECTORY_SEPARATOR . 'src';
+$srcDirectory = new RecursiveDirectoryIterator($srcFolder);
+
+$filteredFileList = new FilenameFilter($srcDirectory, '/(?:php)$/i');
+$filteredFileList = new FilenameFilter($filteredFileList, '/^(?!.*(Complex|Exception)\.php).*$/i');
+
+foreach (new RecursiveIteratorIterator($filteredFileList) as $file) {
+    if ($file->isFile()) {
+        include_once $file;
+    }
+}

inc/vendor/markbaker/complex/classes/src/Complex.php

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+<?php
+
+/**
+ *
+ * Class for the management of Complex numbers
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Complex Number object.
+ *
+ * @package Complex
+ *
+ * @method float abs()
+ * @method Complex acos()
+ * @method Complex acosh()
+ * @method Complex acot()
+ * @method Complex acoth()
+ * @method Complex acsc()
+ * @method Complex acsch()
+ * @method float argument()
+ * @method Complex asec()
+ * @method Complex asech()
+ * @method Complex asin()
+ * @method Complex asinh()
+ * @method Complex atan()
+ * @method Complex atanh()
+ * @method Complex conjugate()
+ * @method Complex cos()
+ * @method Complex cosh()
+ * @method Complex cot()
+ * @method Complex coth()
+ * @method Complex csc()
+ * @method Complex csch()
+ * @method Complex exp()
+ * @method Complex inverse()
+ * @method Complex ln()
+ * @method Complex log2()
+ * @method Complex log10()
+ * @method Complex negative()
+ * @method Complex pow(int|float $power)
+ * @method float rho()
+ * @method Complex sec()
+ * @method Complex sech()
+ * @method Complex sin()
+ * @method Complex sinh()
+ * @method Complex sqrt()
+ * @method Complex tan()
+ * @method Complex tanh()
+ * @method float theta()
+ * @method Complex add(...$complexValues)
+ * @method Complex subtract(...$complexValues)
+ * @method Complex multiply(...$complexValues)
+ * @method Complex divideby(...$complexValues)
+ * @method Complex divideinto(...$complexValues)
+ */
+class Complex
+{
+    /**
+     * @constant    Euler's Number.
+     */
+    const EULER = 2.7182818284590452353602874713526624977572;
+
+    /**
+     * @constant    Regexp to split an input string into real and imaginary components and suffix
+     */
+    const NUMBER_SPLIT_REGEXP =
+        '` ^
+            (                                   # Real part
+                [-+]?(\d+\.?\d*|\d*\.?\d+)          # Real value (integer or float)
+                ([Ee][-+]?[0-2]?\d{1,3})?           # Optional real exponent for scientific format
+            )
+            (                                   # Imaginary part
+                [-+]?(\d+\.?\d*|\d*\.?\d+)          # Imaginary value (integer or float)
+                ([Ee][-+]?[0-2]?\d{1,3})?           # Optional imaginary exponent for scientific format
+            )?
+            (                                   # Imaginary part is optional
+                ([-+]?)                             # Imaginary (implicit 1 or -1) only
+                ([ij]?)                             # Imaginary i or j - depending on whether mathematical or engineering
+            )
+        $`uix';
+
+    /**
+     * @var    float    $realPart    The value of of this complex number on the real plane.
+     */
+    protected $realPart = 0.0;
+
+    /**
+     * @var    float    $imaginaryPart    The value of of this complex number on the imaginary plane.
+     */
+    protected $imaginaryPart = 0.0;
+
+    /**
+     * @var    string    $suffix    The suffix for this complex number (i or j).
+     */
+    protected $suffix;
+
+
+    /**
+     * Validates whether the argument is a valid complex number, converting scalar or array values if possible
+     *
+     * @param     mixed    $complexNumber   The value to parse
+     * @return    array
+     * @throws    Exception    If the argument isn't a Complex number or cannot be converted to one
+     */
+    private static function parseComplex($complexNumber)
+    {
+        // Test for real number, with no imaginary part
+        if (is_numeric($complexNumber)) {
+            return [$complexNumber, 0, null];
+        }
+
+        // Fix silly human errors
+        $complexNumber = str_replace(
+            ['+-', '-+', '++', '--'],
+            ['-', '-', '+', '+'],
+            $complexNumber
+        );
+
+        // Basic validation of string, to parse out real and imaginary parts, and any suffix
+        $validComplex = preg_match(
+            self::NUMBER_SPLIT_REGEXP,
+            $complexNumber,
+            $complexParts
+        );
+
+        if (!$validComplex) {
+            // Neither real nor imaginary part, so test to see if we actually have a suffix
+            $validComplex = preg_match('/^([\-\+]?)([ij])$/ui', $complexNumber, $complexParts);
+            if (!$validComplex) {
+                throw new Exception('Invalid complex number');
+            }
+            // We have a suffix, so set the real to 0, the imaginary to either 1 or -1 (as defined by the sign)
+            $imaginary = 1;
+            if ($complexParts[1] === '-') {
+                $imaginary = 0 - $imaginary;
+            }
+            return [0, $imaginary, $complexParts[2]];
+        }
+
+        // If we don't have an imaginary part, identify whether it should be +1 or -1...
+        if (($complexParts[4] === '') && ($complexParts[9] !== '')) {
+            if ($complexParts[7] !== $complexParts[9]) {
+                $complexParts[4] = 1;
+                if ($complexParts[8] === '-') {
+                    $complexParts[4] = -1;
+                }
+            } else {
+                // ... or if we have only the real and no imaginary part
+                //  (in which case our real should be the imaginary)
+                $complexParts[4] = $complexParts[1];
+                $complexParts[1] = 0;
+            }
+        }
+
+        // Return real and imaginary parts and suffix as an array, and set a default suffix if user input lazily
+        return [
+            $complexParts[1],
+            $complexParts[4],
+            !empty($complexParts[9]) ? $complexParts[9] : 'i'
+        ];
+    }
+
+
+    public function __construct($realPart = 0.0, $imaginaryPart = null, $suffix = 'i')
+    {
+        if ($imaginaryPart === null) {
+            if (is_array($realPart)) {
+                // We have an array of (potentially) real and imaginary parts, and any suffix
+                list ($realPart, $imaginaryPart, $suffix) = array_values($realPart) + [0.0, 0.0, 'i'];
+            } elseif ((is_string($realPart)) || (is_numeric($realPart))) {
+                // We've been given a string to parse to extract the real and imaginary parts, and any suffix
+                list($realPart, $imaginaryPart, $suffix) = self::parseComplex($realPart);
+            }
+        }
+        if ($imaginaryPart <> 0.0 && empty($suffix)) {
+            $suffix = 'i';
+        }
+
+        // Set parsed values in our properties
+        $this->realPart = (float) $realPart;
+        $this->imaginaryPart = (float) $imaginaryPart;
+        $this->suffix = strtolower($suffix);
+    }
+
+    /**
+     * Gets the real part of this complex number
+     *
+     * @return Float
+     */
+    public function getReal()
+    {
+        return $this->realPart;
+    }
+
+    /**
+     * Gets the imaginary part of this complex number
+     *
+     * @return Float
+     */
+    public function getImaginary()
+    {
+        return $this->imaginaryPart;
+    }
+
+    /**
+     * Gets the suffix of this complex number
+     *
+     * @return String
+     */
+    public function getSuffix()
+    {
+        return $this->suffix;
+    }
+
+    /**
+     * Returns true if this is a real value, false if a complex value
+     *
+     * @return Bool
+     */
+    public function isReal()
+    {
+        return $this->imaginaryPart == 0.0;
+    }
+
+    /**
+     * Returns true if this is a complex value, false if a real value
+     *
+     * @return Bool
+     */
+    public function isComplex()
+    {
+        return !$this->isReal();
+    }
+
+    public function format()
+    {
+        $str = "";
+        if ($this->imaginaryPart != 0.0) {
+            if (\abs($this->imaginaryPart) != 1.0) {
+                $str .= $this->imaginaryPart . $this->suffix;
+            } else {
+                $str .= (($this->imaginaryPart < 0.0) ? '-' : '') . $this->suffix;
+            }
+        }
+        if ($this->realPart != 0.0) {
+            if (($str) && ($this->imaginaryPart > 0.0)) {
+                $str = "+" . $str;
+            }
+            $str = $this->realPart . $str;
+        }
+        if (!$str) {
+            $str = "0.0";
+        }
+
+        return $str;
+    }
+
+    public function __toString()
+    {
+        return $this->format();
+    }
+
+    /**
+     * Validates whether the argument is a valid complex number, converting scalar or array values if possible
+     *
+     * @param     mixed    $complex   The value to validate
+     * @return    Complex
+     * @throws    Exception    If the argument isn't a Complex number or cannot be converted to one
+     */
+    public static function validateComplexArgument($complex)
+    {
+        if (is_scalar($complex) || is_array($complex)) {
+            $complex = new Complex($complex);
+        } elseif (!is_object($complex) || !($complex instanceof Complex)) {
+            throw new Exception('Value is not a valid complex number');
+        }
+
+        return $complex;
+    }
+
+    /**
+     * Returns the reverse of this complex number
+     *
+     * @return    Complex
+     */
+    public function reverse()
+    {
+        return new Complex(
+            $this->imaginaryPart,
+            $this->realPart,
+            ($this->realPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    public function invertImaginary()
+    {
+        return new Complex(
+            $this->realPart,
+            $this->imaginaryPart * -1,
+            ($this->imaginaryPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    public function invertReal()
+    {
+        return new Complex(
+            $this->realPart * -1,
+            $this->imaginaryPart,
+            ($this->imaginaryPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    protected static $functions = [
+        'abs',
+        'acos',
+        'acosh',
+        'acot',
+        'acoth',
+        'acsc',
+        'acsch',
+        'argument',
+        'asec',
+        'asech',
+        'asin',
+        'asinh',
+        'atan',
+        'atanh',
+        'conjugate',
+        'cos',
+        'cosh',
+        'cot',
+        'coth',
+        'csc',
+        'csch',
+        'exp',
+        'inverse',
+        'ln',
+        'log2',
+        'log10',
+        'negative',
+        'pow',
+        'rho',
+        'sec',
+        'sech',
+        'sin',
+        'sinh',
+        'sqrt',
+        'tan',
+        'tanh',
+        'theta',
+    ];
+
+    protected static $operations = [
+        'add',
+        'subtract',
+        'multiply',
+        'divideby',
+        'divideinto',
+    ];
+
+    /**
+     * Returns the result of the function call or operation
+     *
+     * @return    Complex|float
+     * @throws    Exception|\InvalidArgumentException
+     */
+    public function __call($functionName, $arguments)
+    {
+        $functionName = strtolower(str_replace('_', '', $functionName));
+
+        // Test for function calls
+        if (in_array($functionName, self::$functions)) {
+            $functionName = "\\" . __NAMESPACE__ . "\\{$functionName}";
+            return $functionName($this, ...$arguments);
+        }
+        // Test for operation calls
+        if (in_array($functionName, self::$operations)) {
+            $functionName = "\\" . __NAMESPACE__ . "\\{$functionName}";
+            return $functionName($this, ...$arguments);
+        }
+        throw new Exception('Function or Operation does not exist');
+    }
+}

inc/vendor/markbaker/complex/classes/src/Exception.php

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+<?php
+
+/**
+ * Exception.
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+class Exception extends \Exception
+{
+}

inc/vendor/markbaker/complex/classes/src/functions/abs.php

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+<?php
+
+/**
+ *
+ * Function code for the complex abs() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the absolute value (modulus) of a complex number.
+ * Also known as the rho of the complex number, i.e. the distance/radius
+ *   from the centrepoint to the representation of the number in polar coordinates.
+ *
+ * This function is a synonym for rho()
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The absolute (or rho) value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    rho
+ *
+ */
+function abs($complex)
+{
+    return rho($complex);
+}

inc/vendor/markbaker/complex/classes/src/functions/acos.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acos() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function acos($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $square = clone $complex;
+    $square = multiply($square, $complex);
+    $invsqrt = new Complex(1.0);
+    $invsqrt = subtract($invsqrt, $square);
+    $invsqrt = sqrt($invsqrt);
+    $adjust = new Complex(
+        $complex->getReal() - $invsqrt->getImaginary(),
+        $complex->getImaginary() + $invsqrt->getReal()
+    );
+    $log = ln($adjust);
+
+    return new Complex(
+        $log->getImaginary(),
+        -1 * $log->getReal()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/acosh.php

@@ -0,0 +1,34 @@
+<?php
+
+/**
+ *
+ * Function code for the complex acosh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function acosh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal() && ($complex->getReal() > 1)) {
+        return new Complex(\acosh($complex->getReal()));
+    }
+
+    $acosh = acos($complex)
+        ->reverse();
+    if ($acosh->getReal() < 0.0) {
+        $acosh = $acosh->invertReal();
+    }
+
+    return $acosh;
+}

inc/vendor/markbaker/complex/classes/src/functions/acot.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex acot() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acot($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return atan(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acoth.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex acoth() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acoth($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return atanh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acsc.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex acsc() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acsc($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return asin(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acsch.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex acsch() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acsch($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return asinh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/argument.php

@@ -0,0 +1,28 @@
+<?php
+
+/**
+ *
+ * Function code for the complex argument() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the argument of a complex number.
+ * Also known as the theta of the complex number, i.e. the angle in radians
+ *   from the real axis to the representation of the number in polar coordinates.
+ *
+ * This function is a synonym for theta()
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The argument (or theta) value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    theta
+ */
+function argument($complex)
+{
+    return theta($complex);
+}

inc/vendor/markbaker/complex/classes/src/functions/asec.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex asec() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function asec($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return acos(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/asech.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex asech() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function asech($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return acosh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/asin.php

@@ -0,0 +1,37 @@
+<?php
+
+/**
+ *
+ * Function code for the complex asin() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function asin($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $square = multiply($complex, $complex);
+    $invsqrt = new Complex(1.0);
+    $invsqrt = subtract($invsqrt, $square);
+    $invsqrt = sqrt($invsqrt);
+    $adjust = new Complex(
+        $invsqrt->getReal() - $complex->getImaginary(),
+        $invsqrt->getImaginary() + $complex->getReal()
+    );
+    $log = ln($adjust);
+
+    return new Complex(
+        $log->getImaginary(),
+        -1 * $log->getReal()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/asinh.php

@@ -0,0 +1,33 @@
+<?php
+
+/**
+ *
+ * Function code for the complex asinh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function asinh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal() && ($complex->getReal() > 1)) {
+        return new Complex(\asinh($complex->getReal()));
+    }
+
+    $asinh = clone $complex;
+    $asinh = $asinh->reverse()
+        ->invertReal();
+    $asinh = asin($asinh);
+    return $asinh->reverse()
+        ->invertImaginary();
+}

inc/vendor/markbaker/complex/classes/src/functions/atan.php

@@ -0,0 +1,45 @@
+<?php
+
+/**
+ *
+ * Function code for the complex atan() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+//include_once 'Math/Complex.php';
+//include_once 'Math/ComplexOp.php';
+
+/**
+ * Returns the inverse tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function atan($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\atan($complex->getReal()));
+    }
+
+    $t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal());
+    $uValue = new Complex(1, 0);
+
+    $d1Value = clone $uValue;
+    $d1Value = subtract($d1Value, $t1Value);
+    $d2Value = add($t1Value, $uValue);
+    $uResult = $d1Value->divideBy($d2Value);
+    $uResult = ln($uResult);
+
+    return new Complex(
+        (($uResult->getImaginary() == M_PI) ? -M_PI : $uResult->getImaginary()) * -0.5,
+        $uResult->getReal() * 0.5,
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/atanh.php

@@ -0,0 +1,38 @@
+<?php
+
+/**
+ *
+ * Function code for the complex atanh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function atanh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        $real = $complex->getReal();
+        if ($real >= -1.0 && $real <= 1.0) {
+            return new Complex(\atanh($real));
+        } else {
+            return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
+        }
+    }
+
+    $iComplex = clone $complex;
+    $iComplex = $iComplex->invertImaginary()
+        ->reverse();
+    return atan($iComplex)
+        ->invertReal()
+        ->reverse();
+}

inc/vendor/markbaker/complex/classes/src/functions/conjugate.php

@@ -0,0 +1,28 @@
+<?php
+
+/**
+ *
+ * Function code for the complex conjugate() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the complex conjugate of a complex number
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The conjugate of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function conjugate($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return new Complex(
+        $complex->getReal(),
+        -1 * $complex->getImaginary(),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cos.php

@@ -0,0 +1,34 @@
+<?php
+
+/**
+ *
+ * Function code for the complex cos() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function cos($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\cos($complex->getReal()));
+    }
+
+    return conjugate(
+        new Complex(
+            \cos($complex->getReal()) * \cosh($complex->getImaginary()),
+            \sin($complex->getReal()) * \sinh($complex->getImaginary()),
+            $complex->getSuffix()
+        )
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cosh.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex cosh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function cosh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\cosh($complex->getReal()));
+    }
+
+    return new Complex(
+        \cosh($complex->getReal()) * \cos($complex->getImaginary()),
+        \sinh($complex->getReal()) * \sin($complex->getImaginary()),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cot.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex cot() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function cot($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return new Complex(INF);
+    }
+
+    return inverse(tan($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/coth.php

@@ -0,0 +1,24 @@
+<?php
+
+/**
+ *
+ * Function code for the complex coth() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function coth($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+    return inverse(tanh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/csc.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex csc() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function csc($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return inverse(sin($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/csch.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex csch() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function csch($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return inverse(sinh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/exp.php

@@ -0,0 +1,34 @@
+<?php
+
+/**
+ *
+ * Function code for the complex exp() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the exponential of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The exponential of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function exp($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) {
+        return new Complex(-1.0, 0.0);
+    }
+
+    $rho = \exp($complex->getReal());
+ 
+    return new Complex(
+        $rho * \cos($complex->getImaginary()),
+        $rho * \sin($complex->getImaginary()),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/inverse.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex inverse() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function inverse($complex)
+{
+    $complex = clone Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        throw new \InvalidArgumentException('Division by zero');
+    }
+
+    return $complex->divideInto(1.0);
+}

inc/vendor/markbaker/complex/classes/src/functions/ln.php

@@ -0,0 +1,33 @@
+<?php
+
+/**
+ *
+ * Function code for the complex ln() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the natural logarithm of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The natural logarithm of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function ln($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+        throw new \InvalidArgumentException();
+    }
+
+    return new Complex(
+        \log(rho($complex)),
+        theta($complex),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/log10.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex log10() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the common logarithm (base 10) of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The common logarithm (base 10) of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function log10($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+        throw new \InvalidArgumentException();
+    } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
+        return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix());
+    }
+
+    return ln($complex)
+        ->multiply(\log10(Complex::EULER));
+}

inc/vendor/markbaker/complex/classes/src/functions/log2.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex log2() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the base-2 logarithm of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The base-2 logarithm of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function log2($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+        throw new \InvalidArgumentException();
+    } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
+        return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix());
+    }
+
+    return ln($complex)
+        ->multiply(\log(Complex::EULER, 2));
+}

inc/vendor/markbaker/complex/classes/src/functions/negative.php

@@ -0,0 +1,31 @@
+<?php
+
+/**
+ *
+ * Function code for the complex negative() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the negative of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The negative value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    rho
+ *
+ */
+function negative($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return new Complex(
+        -1 * $complex->getReal(),
+        -1 * $complex->getImaginary(),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/pow.php

@@ -0,0 +1,40 @@
+<?php
+
+/**
+ *
+ * Function code for the complex pow() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns a complex number raised to a power.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @param     float|integer    $power      The power to raise this value to
+ * @return    Complex          The complex argument raised to the real power.
+ * @throws    Exception        If the power argument isn't a valid real
+ */
+function pow($complex, $power)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (!is_numeric($power)) {
+        throw new Exception('Power argument must be a real number');
+    }
+
+    if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) {
+        return new Complex(\pow($complex->getReal(), $power));
+    }
+
+    $rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()));
+    $rPower = \pow($rValue, $power);
+    $theta = $complex->argument() * $power;
+    if ($theta == 0) {
+        return new Complex(1);
+    }
+
+    return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix());
+}

inc/vendor/markbaker/complex/classes/src/functions/rho.php

@@ -0,0 +1,28 @@
+<?php
+
+/**
+ *
+ * Function code for the complex rho() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the rho of a complex number.
+ * This is the distance/radius from the centrepoint to the representation of the number in polar coordinates.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The rho value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function rho($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return \sqrt(
+        ($complex->getReal() * $complex->getReal()) +
+        ($complex->getImaginary() * $complex->getImaginary())
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sec.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sec() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function sec($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return inverse(cos($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/sech.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sech() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function sech($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return inverse(cosh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/sin.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sin() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sin($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\sin($complex->getReal()));
+    }
+
+    return new Complex(
+        \sin($complex->getReal()) * \cosh($complex->getImaginary()),
+        \cos($complex->getReal()) * \sinh($complex->getImaginary()),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sinh.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sinh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sinh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\sinh($complex->getReal()));
+    }
+
+    return new Complex(
+        \sinh($complex->getReal()) * \cos($complex->getImaginary()),
+        \cosh($complex->getReal()) * \sin($complex->getImaginary()),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sqrt.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sqrt() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the square root of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The Square root of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sqrt($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $theta = theta($complex);
+    $delta1 = \cos($theta / 2);
+    $delta2 = \sin($theta / 2);
+    $rho = \sqrt(rho($complex));
+
+    return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
+}

inc/vendor/markbaker/complex/classes/src/functions/tan.php

@@ -0,0 +1,40 @@
+<?php
+
+/**
+ *
+ * Function code for the complex tan() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function tan($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\tan($complex->getReal()));
+    }
+
+    $real = $complex->getReal();
+    $imaginary = $complex->getImaginary();
+    $divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2);
+    if ($divisor == 0.0) {
+        throw new \InvalidArgumentException('Division by zero');
+    }
+
+    return new Complex(
+        \pow(sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
+        \pow(sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/tanh.php

@@ -0,0 +1,35 @@
+<?php
+
+/**
+ *
+ * Function code for the complex tanh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function tanh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+    $real = $complex->getReal();
+    $imaginary = $complex->getImaginary();
+    $divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real);
+    if ($divisor == 0.0) {
+        throw new \InvalidArgumentException('Division by zero');
+    }
+
+    return new Complex(
+        \sinh($real) * \cosh($real) / $divisor,
+        0.5 * \sin(2 * $imaginary) / $divisor,
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/theta.php

@@ -0,0 +1,38 @@
+<?php
+
+/**
+ *
+ * Function code for the complex theta() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the theta of a complex number.
+ *   This is the angle in radians from the real axis to the representation of the number in polar coordinates.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The theta value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function theta($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0) {
+        if ($complex->isReal()) {
+            return 0.0;
+        } elseif ($complex->getImaginary() < 0.0) {
+            return M_PI / -2;
+        }
+        return M_PI / 2;
+    } elseif ($complex->getReal() > 0.0) {
+        return \atan($complex->getImaginary() / $complex->getReal());
+    } elseif ($complex->getImaginary() < 0.0) {
+        return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal())));
+    }
+
+    return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal()));
+}

inc/vendor/markbaker/complex/classes/src/operations/add.php

@@ -0,0 +1,46 @@
+<?php
+
+/**
+ *
+ * Function code for the complex addition operation
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Adds two or more complex numbers
+ *
+ * @param     array of string|integer|float|Complex    $complexValues   The numbers to add
+ * @return    Complex
+ */
+function add(...$complexValues)
+{
+    if (count($complexValues) < 2) {
+        throw new \Exception('This function requires at least 2 arguments');
+    }
+
+    $base = array_shift($complexValues);
+    $result = clone Complex::validateComplexArgument($base);
+
+    foreach ($complexValues as $complex) {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($result->isComplex() && $complex->isComplex() &&
+            $result->getSuffix() !== $complex->getSuffix()) {
+            throw new Exception('Suffix Mismatch');
+        }
+
+        $real = $result->getReal() + $complex->getReal();
+        $imaginary = $result->getImaginary() + $complex->getImaginary();
+
+        $result = new Complex(
+            $real,
+            $imaginary,
+            ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+        );
+    }
+
+    return $result;
+}

inc/vendor/markbaker/complex/classes/src/operations/divideby.php

@@ -0,0 +1,56 @@
+<?php
+
+/**
+ *
+ * Function code for the complex division operation
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Divides two or more complex numbers
+ *
+ * @param     array of string|integer|float|Complex    $complexValues   The numbers to divide
+ * @return    Complex
+ */
+function divideby(...$complexValues)
+{
+    if (count($complexValues) < 2) {
+        throw new \Exception('This function requires at least 2 arguments');
+    }
+
+    $base = array_shift($complexValues);
+    $result = clone Complex::validateComplexArgument($base);
+
+    foreach ($complexValues as $complex) {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($result->isComplex() && $complex->isComplex() &&
+            $result->getSuffix() !== $complex->getSuffix()) {
+            throw new Exception('Suffix Mismatch');
+        }
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            throw new \InvalidArgumentException('Division by zero');
+        }
+
+        $delta1 = ($result->getReal() * $complex->getReal()) +
+            ($result->getImaginary() * $complex->getImaginary());
+        $delta2 = ($result->getImaginary() * $complex->getReal()) -
+            ($result->getReal() * $complex->getImaginary());
+        $delta3 = ($complex->getReal() * $complex->getReal()) +
+            ($complex->getImaginary() * $complex->getImaginary());
+
+        $real = $delta1 / $delta3;
+        $imaginary = $delta2 / $delta3;
+
+        $result = new Complex(
+            $real,
+            $imaginary,
+            ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+        );
+    }
+
+    return $result;
+}

inc/vendor/markbaker/complex/classes/src/operations/divideinto.php

@@ -0,0 +1,56 @@
+<?php
+
+/**
+ *
+ * Function code for the complex division operation
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Divides two or more complex numbers
+ *
+ * @param     array of string|integer|float|Complex    $complexValues   The numbers to divide
+ * @return    Complex
+ */
+function divideinto(...$complexValues)
+{
+    if (count($complexValues) < 2) {
+        throw new \Exception('This function requires at least 2 arguments');
+    }
+
+    $base = array_shift($complexValues);
+    $result = clone Complex::validateComplexArgument($base);
+
+    foreach ($complexValues as $complex) {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($result->isComplex() && $complex->isComplex() &&
+            $result->getSuffix() !== $complex->getSuffix()) {
+            throw new Exception('Suffix Mismatch');
+        }
+        if ($result->getReal() == 0.0 && $result->getImaginary() == 0.0) {
+            throw new \InvalidArgumentException('Division by zero');
+        }
+
+        $delta1 = ($complex->getReal() * $result->getReal()) +
+            ($complex->getImaginary() * $result->getImaginary());
+        $delta2 = ($complex->getImaginary() * $result->getReal()) -
+            ($complex->getReal() * $result->getImaginary());
+        $delta3 = ($result->getReal() * $result->getReal()) +
+            ($result->getImaginary() * $result->getImaginary());
+
+        $real = $delta1 / $delta3;
+        $imaginary = $delta2 / $delta3;
+
+        $result = new Complex(
+            $real,
+            $imaginary,
+            ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+        );
+    }
+
+    return $result;
+}

inc/vendor/markbaker/complex/classes/src/operations/multiply.php

@@ -0,0 +1,48 @@
+<?php
+
+/**
+ *
+ * Function code for the complex multiplication operation
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Multiplies two or more complex numbers
+ *
+ * @param     array of string|integer|float|Complex    $complexValues   The numbers to multiply
+ * @return    Complex
+ */
+function multiply(...$complexValues)
+{
+    if (count($complexValues) < 2) {
+        throw new \Exception('This function requires at least 2 arguments');
+    }
+
+    $base = array_shift($complexValues);
+    $result = clone Complex::validateComplexArgument($base);
+
+    foreach ($complexValues as $complex) {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($result->isComplex() && $complex->isComplex() &&
+            $result->getSuffix() !== $complex->getSuffix()) {
+            throw new Exception('Suffix Mismatch');
+        }
+
+        $real = ($result->getReal() * $complex->getReal()) -
+            ($result->getImaginary() * $complex->getImaginary());
+        $imaginary = ($result->getReal() * $complex->getImaginary()) +
+            ($result->getImaginary() * $complex->getReal());
+
+        $result = new Complex(
+            $real,
+            $imaginary,
+            ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+        );
+    }
+
+    return $result;
+}

inc/vendor/markbaker/complex/classes/src/operations/subtract.php

@@ -0,0 +1,46 @@
+<?php
+
+/**
+ *
+ * Function code for the complex subtraction operation
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Subtracts two or more complex numbers
+ *
+ * @param     array of string|integer|float|Complex    $complexValues   The numbers to subtract
+ * @return    Complex
+ */
+function subtract(...$complexValues)
+{
+    if (count($complexValues) < 2) {
+        throw new \Exception('This function requires at least 2 arguments');
+    }
+
+    $base = array_shift($complexValues);
+    $result = clone Complex::validateComplexArgument($base);
+
+    foreach ($complexValues as $complex) {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($result->isComplex() && $complex->isComplex() &&
+            $result->getSuffix() !== $complex->getSuffix()) {
+            throw new Exception('Suffix Mismatch');
+        }
+
+        $real = $result->getReal() - $complex->getReal();
+        $imaginary = $result->getImaginary() - $complex->getImaginary();
+
+        $result = new Complex(
+            $real,
+            $imaginary,
+            ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+        );
+    }
+
+    return $result;
+}

inc/vendor/markbaker/complex/composer.json

@@ -0,0 +1,77 @@
+{
+    "name": "markbaker/complex",
+    "type": "library",
+    "description": "PHP Class for working with complex numbers",
+    "keywords": ["complex", "mathematics"],
+    "homepage": "https://github.com/MarkBaker/PHPComplex",
+    "license": "MIT",
+    "authors": [
+        {
+            "name": "Mark Baker",
+            "email": "mark@lange.demon.co.uk"
+        }
+    ],
+    "require": {
+        "php": "^5.6.0|^7.0.0"
+    },
+    "require-dev": {
+        "phpunit/phpunit": "^4.8.35|^5.4.0",
+        "phpdocumentor/phpdocumentor":"2.*",
+        "phpmd/phpmd": "2.*",
+        "sebastian/phpcpd": "2.*",
+        "phploc/phploc": "2.*",
+        "squizlabs/php_codesniffer": "^3.3.0",
+        "phpcompatibility/php-compatibility": "^8.0",
+        "dealerdirect/phpcodesniffer-composer-installer": "^0.4.3"
+    },
+    "autoload": {
+        "psr-4": {
+            "Complex\\": "classes/src/"
+        },
+        "files": [
+            "classes/src/functions/abs.php",
+            "classes/src/functions/acos.php",
+            "classes/src/functions/acosh.php",
+            "classes/src/functions/acot.php",
+            "classes/src/functions/acoth.php",
+            "classes/src/functions/acsc.php",
+            "classes/src/functions/acsch.php",
+            "classes/src/functions/argument.php",
+            "classes/src/functions/asec.php",
+            "classes/src/functions/asech.php",
+            "classes/src/functions/asin.php",
+            "classes/src/functions/asinh.php",
+            "classes/src/functions/atan.php",
+            "classes/src/functions/atanh.php",
+            "classes/src/functions/conjugate.php",
+            "classes/src/functions/cos.php",
+            "classes/src/functions/cosh.php",
+            "classes/src/functions/cot.php",
+            "classes/src/functions/coth.php",
+            "classes/src/functions/csc.php",
+            "classes/src/functions/csch.php",
+            "classes/src/functions/exp.php",
+            "classes/src/functions/inverse.php",
+            "classes/src/functions/ln.php",
+            "classes/src/functions/log2.php",
+            "classes/src/functions/log10.php",
+            "classes/src/functions/negative.php",
+            "classes/src/functions/pow.php",
+            "classes/src/functions/rho.php",
+            "classes/src/functions/sec.php",
+            "classes/src/functions/sech.php",
+            "classes/src/functions/sin.php",
+            "classes/src/functions/sinh.php",
+            "classes/src/functions/sqrt.php",
+            "classes/src/functions/tan.php",
+            "classes/src/functions/tanh.php",
+            "classes/src/functions/theta.php",
+            "classes/src/operations/add.php",
+            "classes/src/operations/subtract.php",
+            "classes/src/operations/multiply.php",
+            "classes/src/operations/divideby.php",
+            "classes/src/operations/divideinto.php"
+        ]
+    },
+    "minimum-stability": "dev"
+}

inc/vendor/markbaker/complex/examples/complexTest.php

@@ -0,0 +1,154 @@
+<?php
+
+use Complex\Complex as Complex;
+
+include('../classes/Bootstrap.php');
+
+echo 'Create', PHP_EOL;
+
+$x = new Complex(123);
+echo $x, PHP_EOL;
+
+$x = new Complex(123, 456);
+echo $x, PHP_EOL;
+
+$x = new Complex(array(123,456,'j'));
+echo $x, PHP_EOL;
+
+$x = new Complex('1.23e-4--2.34e-5i');
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Add', PHP_EOL;
+
+$x = new Complex(123);
+$x->add(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->add(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->add(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->add(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->add(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->add(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Subtract', PHP_EOL;
+
+$x = new Complex(123);
+$x->subtract(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->subtract(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->subtract(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->subtract(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->subtract(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->subtract(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Multiply', PHP_EOL;
+
+$x = new Complex(123);
+$x->multiply(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->multiply(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->multiply(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->multiply(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->multiply(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->multiply(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Divide By', PHP_EOL;
+
+$x = new Complex(123);
+$x->divideBy(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->divideBy(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideBy(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideBy(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideBy(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideBy(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Divide Into', PHP_EOL;
+
+$x = new Complex(123);
+$x->divideInto(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->divideInto(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideInto(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideInto(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideInto(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideInto(new Complex(0, -1));
+echo $x, PHP_EOL;

inc/vendor/markbaker/complex/examples/testFunctions.php

@@ -0,0 +1,52 @@
+<?php
+
+namespace Complex;
+
+include('../classes/Bootstrap.php');
+
+echo 'Function Examples', PHP_EOL;
+
+$functions = array(
+    'abs',
+    'acos',
+    'acosh',
+    'acsc',
+    'acsch',
+    'argument',
+    'asec',
+    'asech',
+    'asin',
+    'asinh',
+    'conjugate',
+    'cos',
+    'cosh',
+    'csc',
+    'csch',
+    'exp',
+    'inverse',
+    'ln',
+    'log2',
+    'log10',
+    'rho',
+    'sec',
+    'sech',
+    'sin',
+    'sinh',
+    'sqrt',
+    'theta'
+);
+
+for ($real = -3.5; $real <= 3.5; $real += 0.5) {
+    for ($imaginary = -3.5; $imaginary <= 3.5; $imaginary += 0.5) {
+        foreach ($functions as $function) {
+            $complexFunction = __NAMESPACE__ . '\\' . $function;
+            $complex = new Complex($real, $imaginary);
+            try {
+                echo $function, '(', $complex, ') = ', $complexFunction($complex), PHP_EOL;
+            } catch (\Exception $e) {
+                echo $function, '(', $complex, ') ERROR: ', $e->getMessage(), PHP_EOL;
+            }
+        }
+        echo PHP_EOL;
+    }
+}

inc/vendor/markbaker/complex/examples/testOperations.php

@@ -0,0 +1,34 @@
+<?php
+
+use Complex\Complex as Complex;
+
+include('../classes/Bootstrap.php');
+
+$values = [
+    new Complex(123),
+    new Complex(456, 123),
+    new Complex(0.0, 456),
+];
+
+foreach ($values as $value) {
+    echo $value, PHP_EOL;
+}
+
+echo 'Addition', PHP_EOL;
+
+$result = \Complex\add(...$values);
+echo '=> ', $result, PHP_EOL;
+
+echo PHP_EOL;
+
+echo 'Subtraction', PHP_EOL;
+
+$result = \Complex\subtract(...$values);
+echo '=> ', $result, PHP_EOL;
+
+echo PHP_EOL;
+
+echo 'Multiplication', PHP_EOL;
+
+$result = \Complex\multiply(...$values);
+echo '=> ', $result, PHP_EOL;

inc/vendor/markbaker/complex/license.md

@@ -0,0 +1,25 @@
+The MIT License (MIT)
+=====================
+
+Copyright © `2017` `Mark Baker`
+
+Permission is hereby granted, free of charge, to any person
+obtaining a copy of this software and associated documentation
+files (the “Software”), to deal in the Software without
+restriction, including without limitation the rights to use,
+copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the
+Software is furnished to do so, subject to the following
+conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.