README

PHP library for extended mathematical operations. Its mostly focused on operations with Complex numbers, Quaternions and Linear Algebra.

Key features and advantages

• Improved Math::pow($base, $exponent) function, able to raise any real or complex number to any real or complex exponent
• Support for Complex numbers and Quaternions ( just like Python with NumPy + PyQuaternion + SymPy )
• Physics units conversion (more units to be added...) using (new Quantity(0.7, IAU::parsec))->convert(SI::metre)

Installation

Library is available on Packagist and could be installed using CLI command:

composer require irrevion/science

Usage

If installed via composer include composer generated autoloader and add use irrevion\science\Math\Math statement for example.
If you are not using composer or using a custom folder you can modify and include custom autoloader.
Example:

require_once("../autoloader.php");

use irrevion\science\Helpers\Utils;
use irrevion\science\Math\Operations\Delegator;
use irrevion\science\Math\Math;
use irrevion\science\Math\Entities\{Scalar, Fraction, Imaginary, Complex};

Examples

Scalar is a basic number class:

use irrevion\science\Math\Entities\Scalar;

$n = new Scalar(5);
print("Scalar to string is {$n}\nType of n is ".($n::class)."\n");
// Outputs:
// Scalar to string is 5
// Type of n is irrevion\science\Math\Entities\Scalar

Basic arithmetic operations available:

$sum = $n->add(new Scalar(3));
$diff = $n->subtract(new Scalar(2));
$prod = $n->multiply(new Scalar(10));
$quotient = $n->divide(new Scalar(3));

As mentioned above, significant enhancement of pow() function has been made:

use irrevion\science\Helpers\Utils;
use irrevion\science\Math\Math;
use irrevion\science\Math\Operations\Delegator;
use irrevion\science\Math\Entities\{Scalar, Fraction, Imaginary, Complex};

$x = 2;
$y = 3;
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".Delegator::getType($z)." ) \n";
// Output: 2**3 is 8 ( integer )

$x = new Scalar(25);
$y = new Scalar(2);
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".($z::class)." ) \n";
// Output: 25**2 is 625 ( irrevion\science\Math\Entities\Scalar )

$x = new Scalar(25);
$y = new Scalar(-2);
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".($z::class)." ) \n";
// Output: 25**-2 is 0.0016 ( irrevion\science\Math\Entities\Scalar )

$x = new Scalar(-1.678903);
$y = new Scalar(-2.5);
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".($z::class)." ) \n";
// Output: -1.678903**-2.5 is [8.3827564317097E-17 + -0.27380160345158i] ( irrevion\science\Math\Entities\Complex )
// Vanilla PHP will give you: NAN
// Python will give you: (8.382756431709652e-17-0.2738016034515765j)

$x = new Scalar(Math::E);
$y = new Imaginary(Math::PI);
$z = Math::pow($x, $y);
print "e**πi is {$z} ( ".($z::class)." ) \n";
// Output: e**πi is [-1 + 1.2246467991474E-16i] ( irrevion\science\Math\Entities\Complex )
// Python gives: (-1+1.2246467991473532e-16j)
// Expected: -1 by formulae e**πi+1=0

$x = new Scalar(125);
$y = new Fraction('1/3');
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".($z::class)." ) \n";
// Output: 125**1/3 is 5 ( irrevion\science\Math\Entities\Scalar )

$x = new Scalar(4);
$y = new Complex(2.5, 2);
$z = Math::pow($x, $y);
print "{$x}**{$y} is {$z} ( ".($z::class)." ) \n";
// Output: 4**(2.5+2i) is [-29.845986458754 + 11.541970902054i] ( irrevion\science\Math\Entities\Complex )
// Python gives: (-29.845986458754275+11.541970902053793j)

It is also possible to get all roots of a number

$roots = (new Complex(-64))->roots(3);
print Utils::printR($roots)." \n";
// Output: [[2 + 3.4641016151378i], [-4 + 4.8985871965894E-16i], [2 + -3.4641016151378i]]

So, as you can see, the following operations are supported:

• raise of real number to a real power
• raise of real number to a fractional power (2/3 means cubic root squared)
• raise of negative number to a rational or real power (1/n is n-th root of a number)
• raise of an any number to negative power (rational or real)
• raise of a number to imaginary or complex power
• raise of an any available value (entity-type instance: mixed/numeric, Scalar, Fraction, Imaginary, Complex, ComplexPolar, QuaternionComponent, Quaternion, Vector, etc) at least to positive integer power

Versions history

~dev-main

• Symbolic math implementation started
• Physics: Added Rydberg energy, kilometre, attometre, angstrom and Bohr radius units

v0.0.5

• Matrix inversion implemented (as well as methods for finding cofactor matrix, adjugate, minors, row echelon form, reduced REF, rank)
• Complex power, exponentiation, natural logarythm implemented
• Quaternions added
• Physics: Added units Dalton, Apostilb, Planck energy

v0.0.4

• Vector checking methods added (orthogonal, collinear, coplarar)
• Angle between vectors calculation added
• Physics: Angle units added

v0.0.3

• Matrix determinant implemented
• Physics: New units added (Ohm, Farad, Watt, etc)

v0.0.2

• Added units in physics
• Fixed fallback autoloader
• Implemented search by unit entity in physical unit categories

v0.0.1

• Basic entities implemented
• Composer requirements are met

Documentation

• Math
  • Numbers, Entities & Matrices
    • NaN
    • Scalar
    • Fraction
    • Imaginary
    • Complex
    • ComplexPolar
    • QuaternionComponent
    • Quaternion
    • Vector
    • Matrix
  • Symbolic Math
    • Symbols
    • Operations
    • Expressions
• Physics
  • Quantity
• Helpers
  • Utils - miscellaneous functions toolbox
  • Delegator - type manager and delegator
  • R - array-like object constructor
  • M - 2-dimensional R