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

irrevion / science

Maintainers

Details